Question

Find the Cartesian equation of the following planes:

`vecr.(hati + hatj-hatk) = 2`

Answer 1

It is given that equation of the plane is

`vecr.(hati + hatj-hatk) = 2`

For any arbitrary point P (x, y, z) on the plane, position vector `vecr`is given by,

`vecr = xhati +yhatj-zhatk`

Substituting the value of `vecr` in equation (1), we obtain

`(xhati + yhatj - zhatk).(hati + hatj - hatk) = 2`

=> x + y - z = 2

This is the Cartesian equation of the plane.