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Question

a=i2j+3k,b=2i+3j4k and c=i3j+λk are co-planar if λ

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Solution

we have to given
a=^i2^j+3^k,b=2^i+3^j4^k and c=^i3^j+λ^k

Three vectors are co-planer if
[abc]=0 ---- (i)

Therefore,
[abc]=∣ ∣12323413λ∣ ∣

from (i) and expanding along R1
0=1(3λ12)(2)(2λ+4)+3(63)
3λ12+84λ+9=0
λ+5=0
λ=5

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