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

.


let the vector equally inclined to OX, OY and OZ at angle α.

Then the direction cosine of the vectors are cos α, cos α and cos α.


Because,


Cos2α + Cos2α + Cos2α = 1


3 Cos2α = 1


Cos2α = 1/3



Hence, the direction cosines of the vector which are equally inclined to the axis are


.


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