If three vectors `2hat(i)-hat(j)-hat(k), hat(i)+2hat(j)-3hat(k)` and `3hat(i)+lambda hat(j)+5hat(k)` are coplanar, then the value of `lambda` is

Options

A. `-4`
B. `-2`
C. `-1`
D. `-8`

Answer

D

Explanation

Let `a=2 hati-hatj-hatk, `
`b=hati+2hatj-3hatkand c=3 hati+lamdahatj+5 hatk`
It these vectors are coplanar, then [a b c] =0
`implies|{:(2,-1,-1),(1,2,-3),(3, lamda,5):}|=0`
`implies2(10+3 lamda)+(5+9)-(lamda-6)=0`
`=20+6 lamda+14-lamda +6=0`
`implies5 lamda +40=0 implies lamda=-8`