Mathematics - Vector Question with Solution | TestHub

Equation of line passing through $(5,1,a)$ and $(3,b,1)$ is $$\frac{x-5}{2}=\frac{y-1}{1-b}=\frac{z-a}{a-1}=\lambda$$ If line crosses $yz-$ plane i.e., $x=0$ $$\begin{array}{rl}& x=2\lambda +5=0\\ & \Rightarrow \lambda =-5/2,\end{array}$$ Since, $y=\lambda (1-b)+1=\frac{17}{2}$ $$\begin{array}{rl}& -\frac{5}{2}(1-b)+1=\frac{17}{2}\\ & b=4\end{array}$$ Also, $z=\lambda (a-1)+a=-\frac{13}{2}$ $$\begin{array}{rl}& -\frac{5}{2}(a-1)+a=-\frac{13}{2}\\ & \Rightarrow a=6\end{array}$$