Question

Find the vector and Cartesian equations of a plane which passes through the point (1, 4, 6) and normal vector to the plane is `(hati -2hatj+hat k) `

Answer 1

Equation`(vecr-veca)*vecn=0`
`vecr-(hati+4hatj+6hatk))*(hati-2hatj+hatk)=0`
`vecr=xhati+yhatj+zhatk`
`((x-1)hati+(y-4)hatj+(z-6)hatk)*(hati-2hatj+hatk)=0`
`(x-1)-2(y-4)+z-6=0`
`x-2y+7-1+8-6=0`
`x-2y+z+1=0`.