Question

multiple choice question
identify a relation among the direction cosines of a force f in space.
o $cos^{2}\theta_{x}-cos^{2}\theta_{y}-cos^{2}\theta_{z}=1$
o $cos\theta_{x}-cos\theta_{y}-cos\theta_{z}=1$
o $cos\theta_{x}+cos\theta_{y}+cos\theta_{z}=1$
o $cos^{2}\theta_{x}+cos^{2}\theta_{y}+cos^{2}\theta_{z}=1$
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Explanation:

Step1: Recall direction - cosine property

In three - dimensional space, for the direction cosines of a vector (or force in this case), if $\cos\theta_x$, $\cos\theta_y$, and $\cos\theta_z$ are the direction cosines along the $x$, $y$, and $z$ axes respectively, by the property of direction cosines, we have the relation $\cos^{2}\theta_x+\cos^{2}\theta_y + \cos^{2}\theta_z=1$.

Answer:

D. $\cos^{2}\theta_x+\cos^{2}\theta_y+\cos^{2}\theta_z = 1$