Question

What is the direction of a vector with an x component of -12 m and a y component of 21 m?

Answer 1

Answer:

$Direction= 119.74^\circ$

Explanation:

Displacement Vector

The displacement, as every vector, has a magnitude r and a direction angle θ measured from the positive x-axis.

If we know the x-y components of the displacement, the magnitude and angle can be calculated by the equations:

$r=\sqrt{x^2+y^2}$

$\displaystyle \tan\theta=\frac{y}{x}$

The coordinates of the given vector are x=-12 m, y=21 m, thus:

$\displaystyle \tan\theta=\frac{21}{-12}=-1.75$

$\theta=tan^{-1}(-1.75)=-60.26^\circ$

Since the vector lies in the second quadrant, we add 180° to find the correct direction:

$\boxed{Direction=-60.26^\circ+180^\circ= 119.74^\circ}$