If `hati+hatj+muhatk, muhati+hatj+hatk, hati+muhatj+hatk` are coplanar vectors, then sum of all distinct values of `mu` is (A) `0` (B) `2` (C) `-1` (D) `1`

Options

A. 2
B. 0
C. 1
D. -1

Answer

D

Explanation

Given vectors `mu hat(i) + hat(j) +hat(k) , hat(i) muhat(j) + hat(k) , hat(j) + mu hat(k) ` will be coplanar if
`|{:(mu,,1,,1),(1,,mu,,1),(1,,1,,mu):}|=0`
`rArr mu(mu^(2) -1) -1(mu -1) + 1(1-mu) =0`
`rArr (mu -1) [mu , (mu+1) -1-1]=0`
`rArr (mu-1) [mu^(2) + mu-2]=0`
`rArr (mu-1) [(mu +2) (mu-1)]=0`
So sum of tthe distinct real values of
`mu =1 -2=-1`