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BlackZzzverrR [31]
3 years ago
12

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

Physics
1 answer:
Svet_ta [14]3 years ago
4 0

Answer:

Direction= 119.74^\circ

Explanation:

<u>Displacement Vector</u>

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}

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