Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are `1/(sqrt(3)),1/(sqrt(3)),1/(sqrt(3))`.

Explanation

Let a vector is equally inclined from OX, OY and OZ axes and makes equal angle `alpha` from each then the direction cosines of the vector will be cos `alpha`, cos `beta` and cos `gamma`.
`therefore cos^(2)alpha + cos^(2) alpha + cos^(2) alpha =1`
`3 cos^(2) alpha =1 `
`implies cos^(2) alpha =(1)/(3) implies cos alpha =pm (1)/(sqrt(3))`
Therefore, the direction cosines of the vector equally inclined from OX, OY and OZ-axis are :
`(1)/(sqrt(3)),(1)/(sqrt(3)),(1)/(sqrt(3)) or -(1)/(sqrt(3)),-(1)/(sqrt(3)),-(1)/(sqrt(3))`.
Hence Proved.