Question

The point of intersection of lines $\frac{x-4}{5}=\frac{y-1}{2}=\frac{z}{1}$ and $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ is

• A. $(-1,-1,-1)$
• B. $(-1,-1,1)$
• C. $(1,-1,-1)$
• D. $(-1,1,-1)$

Answer 1

The correct option is A $(-1,-1,-1)$

The general point on the planes are given by $(5\lambda +4,2\lambda +1,\lambda )$ and $(2\mu +1,3\mu +2,4\mu +3)$ for some constants $\lambda ,\mu$.

Substitute $\lambda =4\mu +3$ in the equation $5\lambda +4=2\mu +1$ we get $\mu =-1$. Hence $(2\mu +1,3\mu +2,4\mu +3)=(-1,-1,-1)$.