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Question

# The point of intersection of the lines x−53=y−7−1=z+21 and x+3−36=y−32=z−64 is-

A
(21,53,103)
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B
(2,10,4)
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C
(3,3,6)
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D
(5,7,2)
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Solution

## The correct option is A (21,53,103)x−53=y−7−1=z+21=λ.............(1)x+3−36=y−32=z−64=μ.............(2)general point on line (1) is (3λ+5,−λ+7,λ−2)general point on line (2) is (−36μ−3,2μ+3,4μ+6)Equating x coordinate3λ+5=−36μ−33λ+36μ+8=0................(iii)Equating y coordinate−λ+7=2μ+3λ+2μ−4=0................(iv)Doing 1×(iii)−3×(iv) By solving equations (iii) and (iv) , we getμ=−23and λ=163Now by putting values of λ in general point of line (1) orμ in general point of line (2) point of intersection of line (1) and (2) is (21,53,103)Therefore option (A) is Correct.

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