Explain with definition and example of Cross Product of Vectors.
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Given:
Cross product of vectors.
Required:
To define and explain the cross product of vectors.
Explanation:
Cross product is the binary operation on two vectors in three dimensional space. It again results in a vector which is perpendicular to both the vectors. Cross product of two vectors is calculated by right hand rule.
Right hand rule is nothing but the resultant of any two vectors is perpendicular to the other two vectors. Using cross product, we can also find the magnitude of the resulting vector.
Let
Vector A and Vector B is denoted by
[tex]\vec{A}\times\vec{B}[/tex]and its resultant vector is perpendicular to the vectors A and B.
Cross Product Formula :
[tex]\vec{A}\times\vec{B}=ab\sin\hat{\theta n}[/tex]where n is the unit vector.
Example:
Let
[tex]\begin{gathered} \vec{a}=2i+k \\ \vec{b}=i+j+k \end{gathered}[/tex]So,
[tex]\vec{a}\times\vec{b}=\begin{bmatrix}{i} & {j} & {k} \\ {2} & {0} & {1} \\ {1} & {1} & {1}\end{bmatrix}[/tex][tex]\begin{gathered} =i(-1)-j(2-1)+k(2-0) \\ =-i-j+2k \end{gathered}[/tex]Final Answer:
Cross product is the binary operation on two vectors in three dimensional space.
Related Questions
Which angles are vertical angles and, therefore, congruent? de A\B EF C/D G H O ZA and ZD O ZA and ZG O ZA and ZE O ZA and ZF
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The vewrtical angles are < A and < D
-6 -5-3 - 26- 235-6Find the slope of the line.Slope = m =Enter your answer as an integer or as a reduced fraction in the form A/B.Question HeinVideo Video M Message instructor
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The formula for slope from a graph is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]We pick two points from the graph (x, y) at point 1 & (x, y) at another point
We can pick the x-intercept (where the line touches the x-axis) as the first point, we have the coordinate to be (4, 0)
We can pick the y-intercept (where the line touches the y-axis) as the second point, we have the coordinate to be (0, 3)
We substitute these points into the slope equation above, we have:
[tex]m=\frac{3-0}{0-4}=-\frac{3}{4}[/tex]The slope (m) = -3/4
question:11/2 raised to 3
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Given
We have
[tex](\frac{11}{2})^3[/tex]Required
Find its value
Explanation
here
[tex](\frac{11}{2})^3=\frac{11^3}{2^3}=\frac{11\times11\times11}{2\times2\times2}=\frac{1331}{8}[/tex]so the answer is
[tex]\frac{1331}{8}[/tex]What is the number for the expression once it is simplified? This should not have any exponents. ((64x-⁹y-¹⁵) ⅓)/ ((8²x-¹²y¹⁰)½)
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The expression to simplify is:
[tex]\frac{(64x^{-9}y^{-15})^{\frac{1}{3}}}{(8^2x^{-12}y^{10})^{\frac{1}{2}}}[/tex]We can use the property shown below to simplify it:
[tex](a^m)^n=a^{mn}[/tex]Thus, we can write:
[tex]\begin{gathered} \frac{(64x^{-9}y^{-15})^{\frac{1}{3}}}{(8^2x^{-12}y^{10})^{\frac{1}{2}}} \\ =\frac{(64)^{\frac{1}{3}}(x^{-9})^{\frac{1}{3}}(y^{-15})^{\frac{1}{3}}}{(64)^{\frac{1}{2}}(x^{-12})^{\frac{1}{2}}(y^{10})^{\frac{1}{2}}} \end{gathered}[/tex]64 to 1/3rd power is 4
64 to 1/2 power is 8
Thus, further simplifying, we have:
[tex]\begin{gathered} \frac{(64)^{\frac{1}{3}}(x^{-9})^{\frac{1}{3}}(y^{-15})^{\frac{1}{3}}}{(64)^{\frac{1}{2}}(x^{-12})^{\frac{1}{2}}(y^{10})^{\frac{1}{2}}} \\ =\frac{4x^{-3}y^{-5}}{8x^{-6}y^5} \end{gathered}[/tex]We can use the rule
[tex]\frac{x^a}{x^b}=x^{a-b}[/tex]to bring up all the exponents and get the simplified form:
[tex]\begin{gathered} =\frac{x^{-3}y^{-5}x^6y^{-5}}{2} \\ =\frac{x^3y^{-10}}{2} \end{gathered}[/tex]This is the final answer.
The exponent of x is 3 and the exponent of y is -10.
7. [0/1 Points]DETAILSPREVIOUS ANSWERSOSCOLALG1 6.5.273.Rewrite the expression as an equivalent ratio of logs using the indicated base.log5(16) to base exRefer to the change-of-base formula to rewrite the expression as a ratio of logarithms with base e. What is anothwith base e?Additional MaterialseBookSubmit Answer
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Explanation:
[tex]\begin{gathered} \text{Given: log}_5(16)\text{ } \\ To\text{ convert to base e} \end{gathered}[/tex]Applying change of base formula:
[tex]\begin{gathered} \log _ba\text{ = }\frac{\log_da}{\log_db}\text{ (For converting to base d)} \\ \\ \text{Applying same principle above to the log given:} \\ \log _516\text{ to base e:} \\ \log _516\text{ = }\frac{\log_e16}{\log_e5} \end{gathered}[/tex][tex]\begin{gathered} \text{The ratio of logarithm with base e:} \\ \text{ }\frac{\log_e16}{\log_e5} \end{gathered}[/tex]Joseph is signing up for a gym membership with a one-time fee to join and then a monthly fee to remain a member. Let C represent the total cost of the gym membership over t months. A graph of C is shown below. Write an equation for C then state the slope of the graph and determine its interpretation in the context of the problem.
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Answer:
Explanation:
The slope-intercept form of the equation of a line is generally given as;
[tex]y=mx+b[/tex]where m = slope of the line
b = y-intercept of the line
For the sake of the given problem, we'll use C for y and t for x. So slope-intercept equation will be written as;
[tex]C=mt+b[/tex]We'll use the bel
5. Create a rule (or equation) for the following geometric sequence 25, -100, 400, -1600 . . .
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Geometric Sequence
In a geometric sequence, each term is calculated as the previous term times a constant number called the common ratio.
If we are given the first terms of the sequence, we can find the common ratio by dividing two consecutive terms.
We are given the sequence:
25, -100, 400, -1600
Dividing the second by the first term:
[tex]r=\frac{-100}{25}=-4[/tex]Dividing the third term by the fourth term:
[tex]r=\frac{400}{-100}=-4[/tex]The common ratio is proven to be constant.
The formula to calculate the nth term of a geometric sequence is:
[tex]a_n=a_1\cdot r^{n-1}[/tex]Where a1 is the first term. In our problem a1 = 25.
The rule or equation for the given geometric sequence is:
[tex]a_n=25\cdot(-4)^{n-1}[/tex]Solve each of the given compound inequalities. Enter your answers using interval notation.x−2≤0 or 7x−5≥65 Solution: x−2≤0 and 7x−5≥65 Solution:
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Ok, so
We want to solve the following compound inequalities.
[tex]x-2\leq0\ldots or\ldots7x-5\ge65[/tex]We're going to solve each inequality as follows:
The first inequality:
[tex]\begin{gathered} x-2\leq0 \\ x\leq2 \end{gathered}[/tex]The second one:
[tex]\begin{gathered} 7x-5\ge65 \\ 7x\ge70 \\ x\ge10 \end{gathered}[/tex]And finally, put these solutions in the number line:
The solution in interval notation will be:
(-inf,2]U[10,inf)
The point on the number line represents the value of a . What is the value of -a?_____What is the value of l-al? ______
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The piont given on the number line is (4).
So,
[tex]a=4[/tex]The value of,
[tex]-a=-4[/tex]in the following diagram we kow that AD=BC and <1=<2 which of the three theorems (ASA,SAS or SSS) would be used to justify that ∆ABC=∆CDA explain
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In the following diagram, we know that AD=BC and ∠1=∠2 which of the three theorems (ASA, SAS or SSS) would be used to justify that ∆ABC=∆CDA explain
_________________________________________________
ASA (it's not possible)
SSS (it's not possible)
-_________________________
SAS (side- angle-side)
∆ABC=∆CDA because
Side AD=BC
Angle ∠1=∠2
Side AC is the same for the two triangles.
1.3.AP-4Find the distance d(A,B) between points A and B.A(7. - 4); B(7,2)d(A,B)=(simplify your answer. Type an exact answer, using radicals as needed.)
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Recall that the distance between two points is given as
[tex]\begin{gathered} d\text{ = }\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{where (x}_1,y_1)\text{ = (7, -4) and (x}_2,y_2)\text{ = }(7,\text{ 2)} \\ \text{Thus, d = }\sqrt{(7-7)^2+(2-(-4))^2} \\ d\text{ = }\sqrt{0+6^2} \\ d\text{ = }\sqrt{36} \\ d\text{ = 6 units} \end{gathered}[/tex]Solve for xxx. Enter the two solutions from least to greatest.(x+7)^2 - 49 = 0
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Solution:
Consider the following quadratic equation:
[tex](x+7)^2-49=0[/tex]solving for the square, this is equivalent to:
[tex](x+7)^2=49[/tex]Taking the square root of both sides of the equation, we obtain:
[tex]x+7=\pm\sqrt[]{49}[/tex]this is equivalent to:
[tex]x+7=\pm7[/tex]so, solving for x, we get two solutions:
Solution 1:
[tex]x=-7+7=0[/tex]Solution 2:
[tex]x=-7-7\text{ = -14}[/tex]So that the correct answer is:
[tex]x=0[/tex][tex]x=\text{-14}[/tex]all of the following illustrate lineear equation in two variables except______.
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Given:
Linear Equation:
A linear equation in two variables is an equation which is expressed in the form of ax+by+c=0 where x and y are variables and a,b,c are constants.
Hence, from the given options:
A) y =x+3 is of the form of ax+by+c = 0 so it is linear.
B) 5x-3y=7 is also linear
C)
[tex]x^2=16[/tex]This is not of the form of ax+by+c=0 so it is non linear.
D)x =7 + 2y is of the form ax+by+c=0 so it is linear.
Hence, option C is not linear out of all the options.
Based on the results of the simulation, how likely is it to get at least tails in 40 flips of a fair coin? There is only a 4% chance of getting at least 26 tails in 40 flips of a fair coin. There is only a 1% chance of getting least 26 tails in 40 flips of a fair coin. a There is a 65% chance of getting at least 26 tails in 40 flips of a fair coin. There is a 50% chance of getting at least 26 tails in 40 flips of a fair coin.
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Step 1: Find the proportion of 40 that is 26.
Let the proportion be x.
Then, we must have
[tex]x=\frac{26}{40}=0.65[/tex]Step 2: Find the probability of getting at least 26 tails in 40 flips of the fair coin
From the simulation, the proportions that are at least 0.65 are 4 in number
[tex]\begin{gathered} Pr(at\text{ least 0.65) }=\text{ Pr(0.65) + Pr(0.7)} \\ 1+3\text{ = 4} \end{gathered}[/tex]The total number of tails is 100.
Therefore,
[tex]\frac{4}{100}=4percent[/tex]The correct answer is this:
There is only a 4% chance of getting at least 26 tails in 40 flips of a fair coin
For question 4 find F -1 (x), the inverse of F(x)
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ANSWER
F⁻¹(x) = 6(x - 3)
EXPLANATION
To find the inverse function we have to clear x as a function of f. In this function
[tex]F(x)=\frac{x}{6}+3[/tex]the first step is to subtract 3 from both sides of the equation:
[tex]\begin{gathered} F(x)-3=\frac{x}{6}+3-3 \\ F(x)-3=\frac{x}{6} \end{gathered}[/tex]And then multiply both sides by 6:
[tex]\begin{gathered} 6(F(x)-3)=\frac{x}{6}\cdot6 \\ 6(F(x)-3)=x \end{gathered}[/tex]Finally change the names of x and F(x). x is now F⁻¹(x) and F(x) is now x:
[tex]F^{-1}(x)=6(x-3)[/tex]A relation is plotted as a linear function on the coordinate plane starting at point A (0,3) and ending at point B (2, 7).What is the rate of change for the linear function and what is its initial value?Select from the drop-down menus to correctly complete the statements.The rate of change is 0 and 2 and 4 and 7 and the initial value is 0 and 2 and 3 and 7
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Give the points, we can calcualte the slope, that is, the rate of change, using the following:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]So, using points (0, 3) and (2, 7), we have:
[tex]m=\frac{7-3}{2-0}=\frac{4}{2}=2[/tex]Now, the slope-intercept form for linear graph is:
[tex]y=mx+b[/tex]Where we have m and b is the y-intercept, that is, the value of the function when x = 0, so the initial value.
Using the first point, (0, 3), we have:
[tex]\begin{gathered} y=2x+b \\ 3=2\cdot0+b \\ 3=b \\ b=3 \end{gathered}[/tex]So, the inital value is 3.
That means that The rate of change is 2 and the initial value is 3.
the locus of points whose: (c)sum of the squares of the coordinates is 25
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x^2 +y^2=25
we need to find two numbers
the number must be under 5 because 5^2=25
so the numbers are
3 and 4
3^2=9
4^2=16
9+16=25
x=3
y=4
I didn't know how to do this "Who, if anyone, traveled at a aster speed? Explain."
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Given:
The graph shows the relationship between the total distance Dominique traveled and the time.
The distance Ella traveled after x hours is represented by the equation,
[tex]y=550x..........\left(1\right)[/tex]To find out: who traveled at a faster speed if anyone.
Explanation:
Let us find the equation of the line for Dominique.
Consider two points,
[tex]\lparen0,0),\left(2,1100\right)[/tex]Using the two-point formula,
[tex]\begin{gathered} \frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1} \\ \frac{y-0}{1100-0}=\frac{x-0}{2-0} \\ \frac{y}{1100}=\frac{x}{2} \\ y=\frac{1100}{2}x \\ y=550x..........\left(2\right) \end{gathered}[/tex]It is of the form,
[tex]y=mx+c,\text{ where m is the slope.}[/tex]Since the slope (i.e. speed) of the equation is m = 550 which is equivalent to the slope (i.e speed) of the equation Ella's.
Therefore, both traveled at the same speed.
Final answer:
Both traveled at the same speed.
I have a question my question is: Find the slope of the line through each pair of points.(0, -5), (-9, 2)
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Answer:
-7/9
Explanation:
The slope of a line can be determined by the below equation;
[tex]\text{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]From the question, we've been given x1 = 0, y1 = -5, x2 = -9, and y2 = 2.
So let's go ahead and substitute the given values into our equation;
[tex]\begin{gathered} \text{Slope}=\frac{2-(-5)}{-9-0} \\ =\frac{2+5}{-9} \\ =-\frac{7}{9} \end{gathered}[/tex]So the slope of the line is -7/9
Choose ALL answers that describe the polygon GHIJ if m
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Answer: Provided the GHIJ, and the following conditions:
[tex]\begin{gathered} m\angle G=m\angle H \\ \\ m\angle I=m\angle J \\ \\ GH\parallel IJ \end{gathered}[/tex]The following figure matches the above conditions:
Therefore the image is a Trapezoid.
new session is here
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hey
[tex]^{9807}[/tex]4(ln(4))-4(ln(1))The answer is 8ln(2) but I don’t know why. I would like to understand the process.
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Given the expression:
[tex]4(\ln (4))-4(\ln (1))[/tex]ln(1) = 0
So, what we have left is
[tex]4\ln (4)[/tex]This can be written as:
[tex]\begin{gathered} 4\ln (2^2) \\ =4\times2\ln (2) \\ =8\ln (2) \end{gathered}[/tex]A tree casts a shadow 12 meters long. At the same time, a building 60 meters tall casts a shadow 36 meters long. How tall is the tree? 60 m 12 m 36 m A 180 meters B 21 meters C 20 meters D 19 meters?
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The triangles are similar using that the light from the sun forms the same angle with every object. Then the triangles are similar, and their sides are proportional. If h is the height of the tree then we have
[tex]\begin{gathered} \frac{h}{12}=\frac{60}{36} \\ h=\frac{60\times12}{36} \\ h=20 \end{gathered}[/tex]So, the height of the tree is 20 m
Lines p and q are intersected by liner, as shown below. If mZ1 = 7x - 36 and mZ2 = 5x + 12, for which value of x would p || q? O 97 O 17 0 24 O 83 1 2 3
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Lines p and q are intersected by liner, as shown below. If mZ1 = 7x - 36 and mZ2 = 5x + 12, for which value of x would p || q? O 97 O 17 0 24 O 83 1 2 3
3 + k = 21k? plus the work
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2f = 8 It’s asking me to find an answer the answers aref = 16f = 10f = 6 f = 4
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How many edges are there?A. 7B. not enough informationC. 10D. 15
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Notice that the top and bottom shape is a pentagon.
Recall that a pentagon has 5 edges
Therefore, the total number of edges in the top and bottom is:
[tex]5+5=10[/tex]Notice that 5 edges connects the top and bottom.
Therefore, the total number of edges is given by:
[tex]10+5=15[/tex]Therefore, the correct answer is choice D:
15
Can someone please solve these problems for me if you could do step by step that would rlly help me this is due Feb 14, 2021 please HELP
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For angle x the perpendicular is 12 and hypotenuse is 54.
Determine the angle by using the trigonometry.
[tex]\begin{gathered} \sin x=\frac{12}{54} \\ x=\sin ^{-1}(0.222) \\ =12.826^{\circ} \\ \approx12.8^{\circ} \end{gathered}[/tex]So value of x is 12.8 degree.
Write an equation that passes through the point (6, -2) with a slope of -4. Write your answer in slope-intercept form.
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Given:
a.) An equation that passes through the point (6, -2).
b.) A slope of -4.
Recall, the slope-intercept form:
[tex]\text{ y = mx + b}[/tex]Where,
m = slope
b = y - intercept
x, y = coordinates of the point that pass through the graph
a.) Let's first determine the y-intercept (b). Substitute x, y = 6, -2 and m = -4 in y = mx + b.
[tex]\text{ y = mx + b}[/tex][tex]\begin{gathered} \text{ (-2) = (-4)(6) + b} \\ \text{ -2 = -24 + b} \\ \text{ -2 + 24 = b} \\ \text{ 22 = b }\rightarrow\text{ b = 22} \end{gathered}[/tex]Therefore, b = 22
b.) Let's now complete the equation. Substitute m = -4 and b = 22 in y = mx + b.
[tex]\text{ y = mx + b}[/tex][tex]\begin{gathered} \text{ y = (-4)x + (22)} \\ \text{ y = -4x + 22} \end{gathered}[/tex]Therefore, the equation of the line is y = -4x + 22
Which angles are supplementary?
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Answer:
Step-by-step explanation:
Supplementary angles add up to 180 degrees. SO one flat line is supplementary 180 degrees:
So:
7,6 are supplementary
7,8 are supplementary