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Question
The position vectors of three points are 2→a−→b+3→c,→a−2→b+λ→c and μ→a−5→b, where →a,→b,→c are non-coplanar vectors. The points are coliinear when
The position vectors of three points are 2→a−→b+3→c,→a−2→b+λ→c and μ→a−5→b, where →a,→b,→c are non-coplanar vectors. The points are coliinear when
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Solution
The correct option is D None of these
Let the points A,B and C respectively, then −−→AB=−−→OB−−−→OA=→a−2→b+λ→c−(2→a−→b+3→c)=−→a−→b+(λ−3)→c−−→AC=−−→OC−−−→OA=μ→a−5→b−(2→a−→b+3→c)=(μ−2)→a−4→b−3→cThe points are collinear if −−→AB=t−−→AC⇒−1=t(μ−2),−1=4t,λ−3=−3t⇒−1=t(μ−2),−1=4t,λ−3=−3t and −1=−14(μ−2),λ−3=34⇒μ=6,λ=154
Let the points A,B and C respectively, then
−−→AB=−−→OB−−−→OA=→a−2→b+λ→c−(2→a−→b+3→c)=−→a−→b+(λ−3)→c
−−→AC=−−→OC−−−→OA=μ→a−5→b−(2→a−→b+3→c)=(μ−2)→a−4→b−3→c
The points are collinear if −−→AB=t−−→AC
⇒−1=t(μ−2),−1=4t,λ−3=−3t
⇒−1=t(μ−2),−1=4t,λ−3=−3t and −1=−14(μ−2),λ−3=34
⇒μ=6,λ=154
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