2. Give vector v=< 3,-6 > and w is a vector with a magnitude of 36 and direction 155 degrees.

a. Write the vector v in i, j component form.

b. Find the magnitude and direction of vector v.

c. Find the i, j vector form of w.

d. Find the resultant vector of v+w. This includes its component form, magnitude and direction.

9514 1404 393

Answer:

  a) v = 3i -6j

  b) v ≈ 6.708∠-63.43°

  c) w = -32.627i +15.214j

  d) v+w = -29.627i +9.214j = 31.027∠162.72°

Step-by-step explanation:

Most graphing calculators and many scientific calculators can do arithmetic with vectors, often in the form of complex numbers or arrays. Of course, the usual conversions can be used:

  (r; α) ⇒ (r·cos(α), r·sin(α))

  (x, y) ⇒ (√(x²+y²); atan2(x, y))

where atan2(x, y) is arctan(y/x) quadrant-adjusted for the signs of x and y

__

a) v = 3i -6j

b) v ≈ 6.708∠-63.43°

c) w = -32.627i +15.214j

d) v+w = -29.627i +9.214j = 31.027∠162.72°

__

The first attachment shows the vectors and their sum in component form as complex numbers. For your purpose, the translation is ...

  a +bi ⇒ ai +bj

The second attachment shows the vectors and their sum in polar form (magnitude and direction). I like the A∠B format. You may translate it to whatever form you need, for example, (A; B), A·cis(B), A(cos(B)i +sin(B)j), Ae^(iB), or any other. (The "semicolon format" is used by at least one app to distinguish between rectangular coordinates (a, b) and polar coordinates (A; B).) The angles here are in degrees (not radians), matching the form in the problem statement.

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