Question

Let the foot of the perpendicular of P(2,âˆ’3,1) on the line x+12=yâˆ’33=zâˆ’2âˆ’1 be Q. If direction ratios of the line segment joining P and Q be l,m,n, then which of the following relations are correct ?

A

2l+3m+n=1

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B

2l+3mn=0

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C

l2=m3=n1

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D

l2=m3=n1

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Solution

The correct option is B 2l+3m−n=0 Let Q be the foot of the perpendicular P. PQ will be perpendicular to the given line. If two line segments with direction ratios (a,b,c) and (u,v,w) are perpendicular, then au+bv+cw=0 Direction ratios of PQ is given as l,m,n and the line segment has direction ratios 2,3,−1 ⇒2l+3m−n=0

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