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Question
If the position vectors of P,Q,R are i+j,i−j and ai+bj+ck and P,Q,R are collinear then-
If the position vectors of P,Q,R are i+j,i−j and ai+bj+ck and P,Q,R are collinear then-
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Solution
The correct option is D c=0,a=1,b∈R
→p=^i+^j
→Q=^ı−j
→R=a^i+b^ȷ+c^k
−−→PQ=−2^ȷ−−→PR=(a−1)^ı+(b−1)^ȷ+c^k−−→QR=(a−1)^r+(b+1)^ȷ+c^k
As P,Q,R are collinear,
→PQ=λPR−2^ȷ=λ((a−1)^ı+(b−1)^ȷ+c^k)
Computing the coefficients of ^ı,^ȷ
and ^k.
−2=λ(b−1)
b=−2λ+1
a−1=0c=0
a=1
a=1c=0b∈R
→p=^i+^j
→Q=^ı−j
→R=a^i+b^ȷ+c^k
−−→PQ=−2^ȷ−−→PR=(a−1)^ı+(b−1)^ȷ+c^k−−→QR=(a−1)^r+(b+1)^ȷ+c^k
As P,Q,R are collinear,
→PQ=λPR−2^ȷ=λ((a−1)^ı+(b−1)^ȷ+c^k)
Computing the coefficients of ^ı,^ȷ and ^k.
−2=λ(b−1)
b=−2λ+1
a−1=0c=0
a=1
a=1c=0b∈RSuggest Corrections
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