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Question

The vectors λi+j+2k, i+λjk and 2ij+λk are coplanar if

A
λ=2
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B
λ=1+3
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C
λ=13
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D
λ=0
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Solution

The correct options are
A λ=2
B λ=1+3
C λ=13
The given vectors are coplanar if and only if
∣ ∣λ121λ121λ∣ ∣=0
λ(λ21)(λ+2)+2(12λ)=0
λ36λ4=0
(λ+2)(λ22λ2)=0
λ=2 or λ=2±4+82=1±3

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