Question

Plane 2 is normal to vector 2i-7j+3k and contains point - 6,0,4 find the equation of the plane

Answer 1

If
`P=(x,y,z)` is any point in the plane and
`P_0=(6,0,4)` is the given point, then
`(x-6)\,\mathbf i+y\,\mathbf j+(z-4)\,\mathbf k` will be a vector that lies in the plane.

Now, if
`2\,\mathbf i-7\,\mathbf j+3\,\mathbf k` is normal to the plane, then the plane is given by the equation


`(2\,\mathbf i-7\,\mathbf j+3\,\mathbf k)\cdot((x-6)\,\mathbf i+y\,\mathbf j+(z-4)\,\mathbf k)=0`

`2(x-6)-7y+3(z-4)=0`

`2x-7y+3z=24`