If vector r wiith dc's l,m,n is equally inclined to the coordinate axes, then the total number of such vectors is

Options

A. 4
B. 6
C. 8
D. 2

Answer

C

Explanation

Given vector r with direction cosines l,m,n is equally inclined to the coordinates axes.
`:. L = m = n "…"(i)`
`:' l^(2) + m^(2) + n^(2) = 1`
`l^(2) + l^(2) + l^(2) = 1` [from Eq. (i)]
`rArr 3l^(2) = 1 rArr l^(2) = 1/3`
`rArr l = +- 1/(sqrt(3))`
`l = m = n = +-1/(sqrt(3))`
Now, vector `r = |r| (+-1/(sqrt(3)) hati +1/(sqrt(3))hatj+- 1/(sqrt(3))hatk)`
Since, each has 2 choices i.e, `l = m = n =1/(sqrt(3))`
`:.` Total number of such vectors `= 2^(3) = 8`