(d) Let a = λi+j+k b =i+λj−k c = 2i - j + λk If these vectors are coplanar, then [a b c] = 0 ⇒|
λ
1
1
1
λ
−1
2
−1
λ
|=0 Expanding along R1, λ(λ2−1)−1(λ+2)+1(−1−2λ)=0 ⇒λ3−λ−λ−2−1−2λ=0 ⇒λ3−4λ−3=0 ⇒λ2(λ+1)−λ(λ+1)−3(λ+1)=0 ⇒(λ+1)(λ2−λ−3)=0 ∴λ+1=0 and λ2−λ−3=0 ⇒λ=−1 and λ=