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,m is equally inclined to the coordinate axes.
`thereforel=m=n` . . . (i)
`becausel^(2)+m^(2)+n^(2)=1`
`l^(2)+l^(2)+l^(2)=1` [from eq. (i)]
`implies3l^(2)=1impliesl^(2)=(1)/(3)`
`impliesl=+-(1)/(sqrt(3))`
`thereforel=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))`
`therefore` Total numbe rof such vectors`=2^3=8`