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Question

Consider a plane x + y - z = 1 and the point A(1, 2, -3). A line L has the equation x = 1 + 3r, y = 2 – r, z = 3 + 4r.
The coordinate of a point B of line L, such that AB is parallel to the plane, is


  1. 4, 1, 7

  2. -8, 5, -9

  3. 10, -1, 15

  4. -5, 4, -5


Solution

The correct option is B

-8, 5, -9


Consider a plane x + y - z = 1 and the point A(1, 2, -3). A line L has the equation x = 1 + 3r, y = 2 – r, z = 3 + 4r.
The coordinate of a point B of line L, such that AB is parallel to the plane, is
Line x13=y21=z34=r,A(1,2,3)
Any point say B=3r+1,2r,3+4r (on the line L)
¯¯¯¯¯¯¯¯AB=3r,r,4r+6
Hence ¯¯¯¯¯¯¯¯AB is parallel to x+yz=1
Hence, 3r - r - 4r - 6 = 0
2r=6r=3
Hence B is -8, 5, -9

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