Given -

To find – The vector equation of the line passing through the origin 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