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Question

If the points with position vectors (^j+^k),4^i+5^j+λ^k,3^i+9^j+4^k and 4^i+4^j+4^k are coplanar, then the value of λ is

A
-1
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B
\N
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C
1
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D
None of these
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Solution

The correct option is C 1
Let the four points be P, Q, R, S respectively. The
PQ=4^i+6^j+(λ+1)^k,QR=^i+4^j+(4λ)^k,RS=7^i5^j+0^k,
The given points are coplanar, therefore PQ,QR,RS are coplanar and so [PQ,QR,RS]=0
∣ ∣46λ+1144λ750∣ ∣=0λ=1

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