1. The problem statement, all variables and given/known data Find out if the following planes and lines intersect. If they intersect, state the point of intersection Plane: 2x + y + 3z = 10 Line: Passing through the point A(1, 5, 1) and B(0, 4, 2) 2. Relevant equations 3. The attempt at a solution I have solved the problem, but am unsure if my working/result is correct.. first we have to find the equation for the line: [x,y,z]=(0,4,2)+t[1,5,1] Equation of the line: x=1t y=4+5t z=2+t We have to know check if they intersect: 2x + y + 3z = 10 Substitute the line equation in the line : 2(t)+(4+5t) + 3(2+t) = 10 2t+4+5t+6+3t=10 10t+10=10 10t=0 t=0 The lines and the plane intersect, since t is a number (0). Find the point of intersection Substitute the value of t into the parametric equations: x=1(0) x = 0 y=4+5(0) y = 4 z=2+(0) z = 2 so the point of intersection is (0,4,2)..but this is the point given in the original question..I am very confused over here...any help is much appreciated Thanks!