A vector v is equally inclined to the x-axis, | vedclass

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Question

(C) Let the vector $v$ make an angle $\alpha$ with each of the three axes. Then the direction cosines of $v$ are $\langle \cos \alpha, \cos \alpha, \c

Vedclass · Accepted Answer

$\langle \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}} \rangle$ or $\langle -\frac{1}{\sqrt{3}}, -\frac{1}{\sqrt{3}}, -\frac{1}{\sqrt{3}} \rangle$

Vedclass · Answer

(C) Let the vector $v$ make an angle $\alpha$ with each of the three axes. Then the direction cosines of $v$ are $\langle \cos \alpha, \cos \alpha, \cos \alpha \rangle$. We know that for any vector,the sum of the squares of its direction cosines is $1$: $\cos^2 \alpha + \cos^2 \alpha + \cos^2 \alpha = 1$ $3 \cos^2 \alpha = 1$ $\cos^2 \alpha = \frac{1}{3}$ $\cos \alpha = \pm \frac{1}{\sqrt{3}}$ Therefore,the direction cosines are $\langle \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}} \rangle$ or $\langle -\frac{1}{\sqrt{3}}, -\frac{1}{\sqrt{3}}, -\frac{1}{\sqrt{3}} \rangle$.

$A$ vector $v$ is equally inclined to the $x$-axis,$y$-axis,and $z$-axis respectively. Its direction cosines are:

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