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Determine the angles made by the vector V = - 36i + 15j with the positive x- and y-axes. Write the unit vector n in the direction of V.
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Determine the angles made by the vector V = - 36i + 15j with the positive x- and y-axes. Write the unit vector n in the direction of V.

User Kishore Kumar
by
6.4k points

1 Answer

4 votes

Answer:

157.38° CCW from +x axis

67.38° CCW from +y axis

n = (12/13)i +(5/13)j

Step-by-step explanation:

The reference angle is ...

arctan(15/36) ≈ 22.62° . . . . CW from the -x axis

The signs of the component vectors indicate this is a 2nd-quadrant vector, so the angles of interest are ...

157.38° CCW from +x axis

67.38° CCW from +y axis

The unit vector will be ...

n = cos(157.38°)i +sin(157.38°)j

n = (12/13)i +(5/13)j

User Travis Troyer
by
6.5k points
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