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

• A. 10, -1, 15
• B. -5, 4, -5
• C. 4, 1, 7
• D. -8, 5, -9

Answer 1

The correct option is D

-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 $\frac{x-1}{3}=\frac{y-2}{-1}=\frac{z-3}{4}=r,A(1,2,-3)$
Any point say $B=3r+1,2-r,3+4r$ (on the line L)
$\overline{AB}=3r,-r,4r+6$
Hence $\overline{AB}$ is parallel to $x+y-z=1$
Hence, 3r - r - 4r - 6 = 0
$2r=-6\Rightarrow r=-3$
Hence B is -8, 5, -9