The coordinates of the point where the line segment joining $A(5, 1, 6)$and B (3, 4, 1) crosses the yz plane are

Suppose yz-plane divides the line segment joining A and B in the ratio $\lambda :1$. The coordinates of 
the point C of division are $\left(\frac{3\lambda +5}{\lambda +1},\frac{4\lambda +1}{\lambda +1},\frac{\lambda +6}{\lambda +1}\right)$
This point lies on yz-plane,
$\therefore \frac{3\lambda +5}{\lambda +1}=0\Rightarrow \lambda =-\frac{5}{3}$
Hence, the coordinates of C are $\left(0,\frac{17}{2},-\frac{13}{2}\right)$.