A vector r is inclined at equal angles to OX,OY and OZ If the magnitude of is 9 units then is equal to

Options

A. `sqrt(hati+hatj+hatk)`
B. `-sqrt3(hati+hatj+hatk)`
C. `3sqrt3(hati+hatj+hatk)`
D. None of these

Answer

C

Explanation

Let `vecr` be inclined at an angle `alpha` to each axis
`therefore" "l=m=n=cosalpha`
`rArrl^2+m^2+n^2=1`
`rArr" "3cos^2alpha=1rArrcosalpha=1/sqrt3`
Given , | |=9
`therefore" "vecr=|vecr(lhati+mhatj+nhatk)`
`=9(1/sqrt3hati+1/sqrt3hatj+1/sqrt3hatk)=3sqrt3(hati+hatj+hatk)`