The point of intersection of the line x+1= y+3 3 = -z+2 2 with the plane 3 x+4 y+5 z=10 is

Step-by-step solution

Let x+1 1 = y+3 3 = -z+2 2 =k Thus, any point on this line will have co-ordinates. x=k-1, y=3 k-3, z=-2 k+2 This line intersects the plane 3 x+4 y+5 z=10 Since, the value of x, y, z must satisfy equation of plane. array ll & 3(k-1)+4(3 k-3)+5(-2 k+2)=10 & 3 k-3+12 k-12+10-10 k=10 & 5 k-5=10 & k=3 array The point of intersection is (x, y, z) aligned & x=3-1, y=3 3-3, z=-2 3+2 & (x, y, z)=(2,6,-4) aligned