Finding a projection from point A (2,-1,3) in the x-3y-z-13 = 0
We know two things about :
- As the projection is orthogonal, is orthogonal to the plane.
- lies in the plane :
Luckily, the equation of the plane gives us a vector which is orthogonal to the plane : . As and are both orthogonal to the plane, they share the same direction that is to say that there exists a real number such that .
As and we have four equations :
Substituting and in will give you the value of from which you'll get . Good luck