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Q.

Let the position vectors of the points P and Q be 4i^+j^+λk^ and 2i^−j^+λk^ respectively. Vector i^−j^+6k^ is perpedicular to the plane containing the origin and the points P and Q. Then λ=

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a

-12

b

12

c

1

d

None of these

answer is A.

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Detailed Solution

A vector perpendicular to the plane of O, P and Q is OP→×OQ→OP→×OQ→=i^j^k^41λ2−1λ=2λi^−2λj^−6k^Therefore i^−j^+6k^ is parallel to 2λi^−2λj^−6k^12λ=−1−2λ=6−6λ=−12

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