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Q11  Show that the direction cosines of a vector equally inclined to the axes OX, OY  and OZ are \pm \left ( \frac{1}{\sqrt 3 } , \frac{1}{\sqrt 3 } , \frac{1}{\sqrt 3 } \right )

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best_answer

Let a vector \vec a is equally inclined to axis OX, OY  and OZ.

let direction cosines of this vector be 

cos\alpha,cos\alpha \:and \:cos\alpha

Now 

cos^2\alpha+cos^2\alpha +cos^2\alpha=1

cos^2\alpha=\frac{1}{3}

cos\alpha=\frac{1}{\sqrt{3}}

Hence direction cosines are:

\left ( \frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}} \right ).

Posted by

Pankaj Sanodiya

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