Find the vector equation of the line passing through the point with position vector and perpendicular to the plane

Given - and the vector has position vector

To find – The vector equation of the line passing through (1, - 2, 5) and perpendicular to the given plane

Tip – The equation of a plane can be given by where is the normal of the plane

A line parallel to the given plane will be in the direction of the normal and will have the direction ratios same as that of the normal.

Formula to be used – If a line passes through the point (a, b, c) and has the direction ratios as (a’, b’, c’), then its vector equation is given by where λ is any scalar constant

The required equation will be for some scalar λ