Answer :

Given :


Equation of plane : 2x + 4y - z = 1


Equation of line :



To Find : Point of intersection of line and plane.


Let P(a, b, c) be point of intersection of plane and line.


As point P lies on the line, we can write,



a = 2k+1, b = -3k+2, c = 4k-3 ………(1)


Also point P lies on the plane


2a + 4b – c = 1


2(2k+1) + 4(-3k+2) – (4k-3) = 1 …..from (1)


4k + 2 – 12k + 8 – 4k + 3 = 1


-12k = -12


k = 1


,




Therefore, co-ordinates of point of intersection of given line and plane are


P ≡


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