The direction cosines of a vector `vecr` which is equally inclined with OX,OY and OZ are

Options

A. `+-1/(sqrt(3)),+-1/(sqrt(3)),+-1/(sqrt(3))`
B. `+-1/3,+-1/3,+-1/3`
C. `+-1/(sqrt(2)),+-1/2,+-1/2`
D. none of these

Answer

A

Explanation

Let `l,m,n` be the direction cosines of `vecr`. Since `vecr` is equally inclined with `OX,OY` and `OZ`.
`:.l=m=n [ :' alpha=beta=gammaimpliescos alpha=cos beta=cos gamma]`
Now `l^(2)+m^(2)+n^(2)=1implies3l^(2)=1impliesl=+-1/(sqrt(3))`
Hence direction cosines of `vecr` are `+-1/(sqrt(3)),+-1/(sqrt(3)),-1/(sqrt(3))`