Question

Consider the plane $\pi :x+y=z$, point A(1, 2, -3) and a line $L:\frac{x-1}{3}=\frac{y-2}{-1}=\frac{z-3}{4}$

The coordinates of a point B on L such that AB is parallel to the plane is ___

• A. (8, 5, -9)
• B. (-8, 5, 9)
• C. (-8,-5, 9)
• D. (-8,5, -9)

Answer 1

The correct option is D

(-8,5, -9)

$B=(3\lambda +1,-\lambda +2,4\lambda +3)$
$1\left(3\lambda \right)+1(-\lambda )-1(4\lambda +6)=0$
$\lambda =-3$
$B=(-8,5,-9)$
Equation is $a(x-1)+b(y-2)+c(z-3)=0$
It passes through $(1,2,-3)\Rightarrow c=0$
and $3a-b=0\Rightarrow a=1andb=3$
$(x-1)+3(y-2)=0$