If vector `hat(i)+hat(j)+hat(k), hat(i)-hat(j)+hat(k)` and `2hat(i)+3hat(j)+lambda hat(k)` are coplanar, then `lambda` is equal to

Options

A. `-2`
B. 3
C. 2
D. `-3`

Answer

C

Explanation

Since, vectors `hati+hatj+hatk, hati-hatj+hatk" and "2hati+3hatj+lamdahatk` are coplanar, therefore
`|{:(1,1,1),(1,-1,1),(2,3,lamda):}|=0`
`rArr" "2(-lamda-3)-1(lamda-2)+1(3+2)=0`
`rArr" "-lamda-3 -lamda+2+5=0`
`rArr" "2lamda=4lamda=2`