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Question
The position vectors of the points A,B,C and D are 3^i−2^j−^k,2^i+3^j−4^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
The position vectors of the points A,B,C and D are 3^i−2^j−^k,2^i+3^j−4^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
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Solution
The correct option is C −(14617)
−−→AB=−^i+5^j−3^k−−→AC=−4^i+3^j+3^k−−→AD=^i+7^j+(λ+1)^k
Vectors −−→AB,−−→AC,−−→AD will be coplanar
⇒∣∣
∣∣−15−3−43317λ+1∣∣
∣∣=0⇒λ=−14617
−−→AB=−^i+5^j−3^k−−→AC=−4^i+3^j+3^k−−→AD=^i+7^j+(λ+1)^k
Vectors −−→AB,−−→AC,−−→AD will be coplanar
⇒∣∣
∣∣−15−3−43317λ+1∣∣
∣∣=0⇒λ=−14617
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