Given that a vector has components (120 m, −60.0 m), find the direction of the vector relative to the positive x-axis.
A) 116º
B) 26.6º
C) −26.6º
D) 122º

Question

Quizplus · Accepted Answer

To find the direction of the vector relative to the positive x-axis, we need to find the angle that the vector makes with the positive x-axis in a counterclockwise direction. We can use trigonometry to do this. The angle θ is given by:
θ = tan⁻¹(y/x)
where x and y are the components of the vector.

θ = tan⁻¹(-60.0 m/120 m) = -26.6º

Note that we get a negative result because the angle is measured in a counterclockwise direction from the positive x-axis. To get the angle in a clockwise direction, we would subtract this value from 360º.

Therefore, the direction of the vector relative to the positive x-axis is 360º - 26.6º = 333.4º, which is equivalent to -26.6º. The closest choice to this answer is C.

Given That a Vector Has Components (120 M, −60