Find the point at which the line x = 3-t ,y = -3t, z = 1-2t intersects the plane x+y-2z = 2 .
How to solve this question?
Is it only replace the x, y and z ?
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plugging $$x=3-t,y=-3t,z=1-2t$$ in the equation of the given plane we get $$3-t-3t-2(1-2t)=2$$ now solve this equation for $t$ we will find no real $t$ thus your line doesn't intersect the plane the line is parallel to the plane