Find the vector equation of the plane which is at a distance of from the origin and its normal vector from the origin is . Also, find its Cartesian form.

Question

Philoid · Accepted Answer

Given, normal vector

Now,

The equation of the plane in normal form is

…… (i)

(where d is the distance of the plane from the origin)

Substituting and d = in (i)

……(ii)

Cartesian Form

For Cartesian Form, substituting in (ii), we get

So, 2x – 3y + 4z = 6, is the Cartesian form