The vector λi + j + 2k, i + λj - k are and 2i - j + λk coplanar if

Question

The vector \(λ \hat i + \hat j + 2 \hat k, \hat i + λ \hat j - \hat k\) are and \(2 \hat i - \hat j + λ \hat k\) coplanar if

A. λ = –2
B. λ = 0
C. λ = 1
D. λ = –1

Answer 1

⇒ λ (λ²-1) -1(λ+2) +2(-1-2 λ)=0

⇒ λ³- λ –λ-2-2-4 λ=0

⇒ λ³- 6λ-4 =0

⇒ (λ+2)( λ²-2 λ-2)=0