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Question

If a line with direction ratio 2:2:1 intersects the line x−73=y−52=z−31 and x−12=y+14=z+13 at A and B then AB=

A
2 units
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B
2 units
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C
3 units
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D
3 units
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Solution

The correct option is C 3 units
x73=y52=z31LetA=(3r1+7,2r1+5,r1+3)x12=y+14=z+13and,LetB=(2r2+1,4r21,3r21)DirectionratiosofAB=(2r23r16,4r22r16,3r2r14)2r23r162=4r22r162=3r2r141r1+2r2=0r1=2and,4r12r16=6r22r182=2r2r2=1A(1,1,1)B=(3,3,2)AB=4+4+1=3Hence,OptionDisthecorrectanswer.

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