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If vector r with dc's l,m, n is equally inclined to the coordinate axes, then the total number of such vectors is 

Answer:

Explanation:

 Given vector  r with  direction cosines l,m,n is equally inclined to the coordinate axes,

$\therefore$     l=m=n ........(i)

$\because$      l²+m²+n²=1

         l²+l²+l²=1  [from E.q,(i)]

 $\Rightarrow$      3l² =l$\rightarrow$ l²=$\frac{1}{3}$

 $\Rightarrow$    $l=\pm\frac{1}{\sqrt{3}}$

$\therefore$     l=m=n= $\pm\frac{1}{\sqrt{3}}$

 Now vector =   $r=|r|\left(\pm \frac{1}{\sqrt{3}}\hat{i}+\frac{1}{\sqrt{3}}\hat{j}\pm\frac{1}{\sqrt{3}}\hat{k}\right)$

 Since, each has 2 choices i.e, l=m=n= $\frac{1}{\sqrt{3}}$

$\therefore$   Total number of such vectors =2³=8