Question

Find the vector and Cartesian equation of the planes that passes through the point (1, 4, 6) and the normal vector to the plane is `hati -2hatj +  hatk`

Answer 1

The position vector of the point (1, 4, 6) is veca = `hati + 4hatj + 6hatk`

The normal vector `vecN`perpendicular to the plane is `vecN = hati - 2hatj + hatk` 

The vector equation of the plane is given by, `(vecr - veca).vecN = 0`       

This is the Cartesian equation of the required plane.