Find the point where the line meets the plane 2x + 4y – z = 1.
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
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