Question

If two lines $\frac{x-1}{1}=\frac{y-2}{k}=\frac{z-3}{1}$ and $\frac{x}{1}=\frac{y}{2}=\frac{z}{k}$ intersect, then the value of $k$ is

• A. $4$
• B. $5$
• C. $2$
• D. $6$

Answer 1

The correct option is C $2$

$\to \frac{x-1}{1}=\frac{y-2}{k}=\frac{2-3}{1}=d........=$ constant

$\therefore (x,y,z)\equiv (d+1,dk+2,d+5)$

$\frac{x}{1}=\frac{y}{2}=\frac{z}{k}=e..............e=$ constant

$\therefore (x,y,z)\equiv (e,2e,ek)$

$\therefore$ (d+1=e) = (dk+2=2e) (d+3=ek)$

$d=e-1$

$(e-1)\left(k\right)+2=2e$

$k=\frac{2e-2}{e-1}=2$

$\therefore k=2$