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11, Show that the direction cosines ofa ...

11, Show that the direction cosines ofa vector equally inclined to the axes OX,0Y and 0Z are `1/sqrt3,1/sqrt3,1/sqrt3`

Text Solution

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Let `alpha` is the angle of the vector equally inclined to the axes OX, OY and OZ.
Then, direction cosines will be `(cosalpha,cosalpha,cosalpha)`.
We know, sum of squares of direction cosines is always 1.
`cos^2alpha+cos^2alpha+cos^2alpha=1`
`=>3cos^2alpha=1`
`=>cosalpha = 1/sqrt3`
So, direction cosines are `(1/sqrt3,1/sqrt3,1/sqrt3)`.
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