Question

If the line through the points $A(k, 1,-1)$ and $B$ $(2 k, 0,2)$ is perpendicular to the line through the points $B$ and $C(2+2 k, k, 1)$, then what is the value of $k$ ?

• A. -1
• B. 1
• C. -3
• D. 3

Answer 1

Answer: (D)

$A(k, 1,-1) B(2 k, 0,2),C(2+2 k, k, 1)$
$A B$ d r' $S=(2 k-k, 0-1,2-(-1)$
$=(k,-1,3)$
$B C$ d r' $S=(2+2 k-2 k, k-0,1-2)$
$=(2, k,-1)$
So $ a_{1} a_{2}+b_{1} b_{2}+c_{1} c_{2}=0$
$k(2)+k(-1)+3(-1)=0$
$2 k+k-3=0$
$k=3$