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Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are

    \[\frac{1}{\sqrt{3}}\]

,

    \[\frac{1}{\sqrt{3}}\]

,

    \[\frac{1}{\sqrt{3}}\]

.
CBSE | Class 12 | Maths | Miscellaneous | NCERT | Vector Algebra
Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are

    \[\frac{1}{\sqrt{3}}\]

,

    \[\frac{1}{\sqrt{3}}\]

,

    \[\frac{1}{\sqrt{3}}\]

.

Firstly,

Let’s assume a vector to be equally inclined to axes OX, OY, and OZ at angle 

    \[\alpha \]

.

Then, the direction cosines of the vector are

    \[\cos \alpha \]

,

    \[\cos \alpha \]

and

    \[\cos \alpha \]

.

Now, we know that

Therefore, the direction cosines of the vector which are equally inclined to the axes are

    \[\frac{1}{\sqrt{3}}\]

,

    \[\frac{1}{\sqrt{3}}\]

,

    \[\frac{1}{\sqrt{3}}\]

.

Hence proved.

i

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