Q. 205.0( 3 Votes )

Find the coordina

Answer :

Given :


Equation of plane : 2x + y + z = 7


Points :


A = (3, -4, -5)


B = (2, -3, 1)


To Find : Point of intersection of line and plane.


Formula :


Equation of line passing through A = (x1, y1, z1) &


B = (x2, y2, z2) is



Equation of line passing through A = (3, -4, -5) & B = (2, -3, 1) is




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


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



a = k+3, b = -k - 4, c = -6k-5 ………(1)


Also point P lies on the plane


2a + b + c = 7


2(k+3) + (-k-4) + (-6k-5) = 7 …..from (1)


2k + 6 – k - 4 – 6k - 5 = 7


-5k = 10


k = -2


,




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


P ≡


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