Line L : 2 x − 2 = b y − 1 = c z + 1 passes through ( 1 , 2 , 3 ) . A parallel line K is a x + 2 = 2 y − 3 = d z + 4 . Find the shortest distance between L and K .

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Mathematics3D-Coordinate GeometryLine ( Equation etc.)Medium2 minQB

MathematicsMediumsingle choice

Line $L : \frac{x - 2}{2} = \frac{y - 1}{b} = \frac{z + 1}{c}$ passes through $(1, 2, 3)$ . A parallel line $K$ is $\frac{x + 2}{a} = \frac{y - 3}{2} = \frac{z + 4}{d}$ . Find the shortest distance between $L$ and $K$ .

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Answer:

Solution:

The point condition gives $b = - 2, c = - 8$ ; parallelism gives $a = - 2, d = 8$ . The distance formula for parallel lines gives $243 /3 = 27 = 33$ .

Stream:JEESubject:MathematicsTopic:3D-Coordinate GeometrySubtopic:Line ( Equation etc.)

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