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Question

A line L passes through a point with position vector a and is perpendicular to the plane containing the two intersecting lines r=b+λp and r=c+μq, where λ,μR. If L intersects a plane rn=d at the point R, then the position vector of the point R is

A
(dan)(p×q)
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B
a+(dan)[p q n] (p×q)
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C
a+[p q n] b+[p q a] c
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D
a+(d+an)[p q n] (p×q)
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Solution

The correct option is B a+(dan)[p q n] (p×q)
Equation of the line L is r=a+t(p×q)
Since L intersects plane rn=d,
(a+t(p×q))n=d
an+t[p q n]=d
t=(dan)[p q n]
Thus, the position vector of R is
r=a+(dan)[p q n](p×q)

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