Question

The equation of a plane passing through a point `3hati-hatj+hatk` and perpendicular to the vector `4hati+2hatj-hatk`?

Answer 1

`4x+2y-z=9`

Explanation:

The family of planes perpendicular to the vector `4hati+2hatj-hatk` has the general scalar equation:

`4x+2y-z=C`

To find the specific scalar equation of the desired plane, substitute the point `(3,-1,1)` and solve for the value of C:

`4(3)+2(-1)-1=C`

`C = 9`

The scalar equation of the desired plane is:

`4x+2y-z=9`