Find the co-ordinates of point where the line (x-3)/-1=(y +4)/1=(z +5)/6 crosses the plane passing through points (7/2, 0,0),(0,7,0) and (0, 0, 7).

Let the coordinates of required point on line is \(\displaystyle (-\lambda+3, \lambda-4,6 \lambda-5)\) for some \(\displaystyle \lambda\) Equation of plane is \(\displaystyle \frac{2 x}{7}+\frac{y}{7}+\frac{z}{7}=1\) \[\therefore 2(-\lambda+3)+\lambda-4+6 \lambda-5=7 \] Gives \(\displaystyle 5 \lambda=10\) i.e. \(\displaystyle \lambda=2\) ∴ Required point is ($\displaystyle 1$, -$\displaystyle 2$, $\displaystyle 7$)