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Question

Let the foot of the perpendicular of P(2,3,1) on the line
x+12=y33=z21 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+3mn=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+3mn=0


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