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Find λ if λi + j + 2k; λj - k and 2i - j + λk are coplanar.

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in Vector algebra by (54.9k points)

Find λ if λi + j + 2k; λj - k and 2i - j + λk are coplanar.

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The condition for coplanarity is

By inspection it is seen that λ = -2 is a root. Therefore,

λ3 - 6λ - 4 = (λ + 2)(λ2 - 2λ - 2)

and λ2 - 2λ - 2 = 0 for λ = 1 ±√3

The required value of λ are

λ1 = -2; λ2 = 1 + √3; λ3 = 1 - √3

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