Given that a vector extends from the origin to (-5.0 cm,8.0 cm),find the direction of the vector from the positive x-axis.
A) $32^{\circ}$
B) $58^{\circ}$
C) $148^{\circ}$
D) $122^{\circ}$

Question

Quizplus · Accepted Answer

To find the direction of the vector from the positive x-axis, we need to use trigonometry.

First, we need to find the length of the vector:

length = sqrt((-5.0 cm)^2 + (8.0 cm)^2) = 9.43398 cm

Now, we can use the inverse tangent function to find the angle between the vector and the x-axis:

angle = tan^-1(8.0 cm / -5.0 cm) = -58.2825 degrees

Since we want the angle between the vector and the positive x-axis, we need to add 180 degrees to get:

angle = 180 - 58.2825 = 121.7175 degrees ≈ 122 degrees

Therefore, the answer is choice D, 122F1F1F1S1F1F1F10.

Given That a Vector Extends from the Origin to (-5 32∘32^{\circ}32∘

Given That a Vector Extends from the Origin to (-5 $32^{\circ}$