Question

Find the Cartesian equation of the following planes:

`vecr.[(s-2t)hati + (3 - t)hatj + (2s + t)hatk] = 15`

Answer 1

`vecr.[(s-2t)hati + (3 - t)hatj + (2s + t)hatk] = 15`  ....(1)

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 `hatr` in equation (1), we obtain

This is the Cartesian equation of the given plane.