Question

If the lines $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{1}$ intersect, then $k=$

• A. $0$
• B. $3$
• C. $\frac{7}{2}$
• D. $-1$

Answer 1

Answer: (C)

$\frac{7}{2}$

we know for two lines to intersect,
$\left|\begin{array}{ccc}{x}_2-x_1& y_2-y_1& z_2-z_1\\ a_1& b_1& c_1\\ a_2& b_2& c_2\end{array}\right|=0$

$\Rightarrow \left|\begin{array}{ccc}2& k+1& 1\\ 2& 3& 4\\ 1& 2& 1\end{array}\right|=0\Rightarrow 2(3-8)-(k+1)(2-4)+1(4-3)$

$\Rightarrow 2k-7=0$

$\Rightarrow k=\frac{7}{2}$