If a vector vec{r} with direction cosines l, | vedclass

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(C) For a vector $\vec{r}$ to be equally inclined to the coordinate axes, the direction cosines must satisfy $|l| = |m| = |n|$.Since $l^2 + m^2 + n^2

Vedclass · Accepted Answer

$8$

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(C) For a vector $\vec{r}$ to be equally inclined to the coordinate axes, the direction cosines must satisfy $|l| = |m| = |n|$.Since $l^2 + m^2 + n^2 = 1$, we substitute $|l| = |m| = |n|$ to get $l^2 + l^2 + l^2 = 1$.This simplifies to $3l^2 = 1$, which gives $l^2 = \frac{1}{3}$.Thus, $l = \pm \frac{1}{\sqrt{3}}$, $m = \pm \frac{1}{\sqrt{3}}$, and $n = \pm \frac{1}{\sqrt{3}}$.Each of the direction cosines $l, m, n$ has $2$ possible values $(\pm \frac{1}{\sqrt{3}})$.Therefore, the total number of such vectors is $2 	imes 2 	imes 2 = 8$.

If a vector $\vec{r}$ with direction cosines $l, m, n$ is equally inclined to the coordinate axes, then the total number of such vectors is

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