Question

Find the cartesian form of the equation of the plane `bar r=(hati+hatj)+s(hati-hatj+2hatk)+t(hati+2hatj+hatj)`

Answer 1

The equation `barr=bara+sbarb+tbarc` represents a plane passing through a point having position vector a and parallel to the vectors b and c .

Here, `bara=hati+hatj, barb=hati-hatj+2hatk and barc=hati+2hatj+hatk`

The given plane is perpendicular to the vector `barn`

Vector equation of the plane in scalar product form is `barr.barn=bara.barn`

`therefore x(-5)+y(1)+z(3)=-4`

`therefore -5x+y+3z=-4`

`therefore 5x-y-3z=4`

which is the cartesian form of the equation of the plane