Question

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 if $K$ equals

• A. $\frac{3}{2}$
• B. $\frac{9}{2}$
• C. $\frac{-2}{9}$
• D. $\frac{-3}{2}$

Answer 1

Answer: (B)

$\frac{9}{2}$

$\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$

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

Two line intersect

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

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

$\Rightarrow 2(3-8)-(k+1)(2-4)-1(4-3)=0$

$\Rightarrow -10+2k+2-1=0$

$\Rightarrow 2k-9=0$

$\Rightarrow k=\frac{9}{2}$