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Question

Find the length of perpendicular from P(2,3,1) to the line x12=y33=z+21

A
5
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B
53114
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C
50
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D
2213
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Solution

The correct option is A 53114
Let take a point on line (2λ+1,3λ+3,λ2)

Direction ratio's of line which is perpendicular to given line,

(2λ+12,3λ+3+3,λ21)

(2λ1,3λ+6,λ3)

And the direction ratio's of given line are 2,3,1.

These two lines are perpendicular, so

(2λ1)2+(3λ+6)3+(λ3)+(1)=0

λ=1914
So point is (2414,1514,914)
So distance between (2414,1514,914) and (1,3,2) is 53114...................(by distance formula)

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