Question

If the straight lines
$\frac{x-1}{k}=\frac{y-2}{2}=\frac{z-3}{3}$ and
$\frac{x-2}{3}=\frac{y-3}{k}=\frac{z-1}{2}$ intersect at a
point, then the integer $k$ is equal to

• A. $2$
• B. $-2$
• C. $-5$
• D. $5$

Answer 1

The correct option is C $-5$

Given, $\frac{x-1}{k}=\frac{y-2}{2}=\frac{z-3}{3}$ and $\frac{x-2}{3}=\frac{y-3}{k}=\frac{z-1}{2}$

Since lines intersect in a point

$\left|\begin{array}{ccc}k& 2& 3\\ 3& k& 2\\ 1& 1& -2\end{array}\right|=0$

$\therefore {2k}^2+5k-25=0$

$\therefore k=-5,\frac{5}{2}$