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Distance between Two Parallel Planes

The lines L...

Question

The lines $L_{1}$ and $L_{2}$ intersect at the point

A

(- 3, 2, 1)

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B

(2, 1, - 3)

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C

(1, - 3, 2)

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D

none of these

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Solution

The correct option is B $(2, 1, - 3)$
The point on the line $L_{1}$ is in the form $(- 3 t - 1, 3 + 2 t, t - 2)$ where $t$ is constant
The point on the line $L_{2}$ is in the form $(s, 7 - 3 s, 2 s - 7)$ where $s$ is constant
At intersection point , both are equal
So by equating , we get $s = - 3 t - 1$ and $2 t + 3 s = 4$
By solving we get $t = - 1$ and $s = 2$
So the point of intersection is $(2, 1, - 3)$

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