Write a vector equation for the line through \((1,2,3)\) with direction vector \((4,-1,0)\).

Does the point \((9,0,3)\) lie on the line \((x,y,z)=(1,2,3)+t(4,-1,0)\)?

Find a direction vector for the line through \(A=(2,-1,4)\) and \(B=(5,3,0)\).

Find the intersection point of the line \((x,y,z)=(1,0,2)+t(2,1,-1)\) with the plane \(x+y+z=6\).