Question

$A=(1,2,3),B=(4,5,7),C=(-4,3,-6),D=(2,k,2)$ are four points. If the lines $AB$ and $CD$ are parallel, then $k=$

• A. $3$
• B. $9$
• C. $-3$
• D. $-9$

Answer 1

The correct option is B $9$

DR's of $\overrightarrow{AB}=(3,3,4)=(a_1,b_1,c_1)$
DR's of $\overrightarrow{CD}=(6,k-3,8)=(a_2,b_2,c_2)$
Given that $\overrightarrow{AB}$ and $\overrightarrow{CD}$ are parallel,so
$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
$\Rightarrow \frac{3}{6}=\frac{3}{k-3}=\frac{4}{8}$
$k-3=6$
$k=9$