Find the vector equation of the line passing through the point `(1,-1,2)` and perpendicular to the plane `2x-y-3z-5=0.`

Explanation

Let `a, b, c` be the direction ratios of the given line.

Since the line passes through the point `(1,-1,2)` is
`frac{x-1}{a}=frac{y+1}{b}=frac{z-2}{c} ldots` (1)

Since this line is perpendicular to the plane `2 x-y+3 z-5=0`, the line is parallel to the normal of the plane.

So, the direction ratios of the line are proportional to the direction ratios of the given plane.


`So , frac{a}{2}=frac{b}{-1}=frac{c}{3}=lambda`

`Rightarrow a=2 lambda ; b=-lambda ; c=3 lambda`


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