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Question

The position vectors of the points A,B,C and D are 3^i2^j^k,2^i+3^j4^k,^i+^j+2^k and 4^i+5^j+λ^k. It is known that these points are coplanar, then λ is equal to

A
(14617)
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B
(13717)
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C
(15417)
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D
None of these
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Solution

The correct option is C (14617)
AB=^i+5^j3^kAC=4^i+3^j+3^kAD=^i+7^j+(λ+1)^k

Vectors AB,AC,AD will be coplanar

∣ ∣15343317λ+1∣ ∣=0λ=14617

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