JEE Main 2021 (Online) 26th February Morning ShiftQuestion 1
Let $(\lambda,2,1)$ be a point on the plane which passes through the point $(4,-2,2)$. If the plane is perpendicular to the line joining the points $(-2,-21,29)$ and $(-1,-16,23)$, then $\left(\frac{\lambda}{11}\right)^{2}-\frac{4\lambda}{11}-4$ is equal to $\_\_\_\_\_\_$ .
3D Geometry
Answer$8$
Solution
Normal $=(1,5,-6)$. Plane: $(x-4)+5(y+2)-6(z-2)=0$. Point $(\lambda,2,1)$: $\lambda+22=0$, $\lambda=-22$. $\frac\lambda{11}=-2$: $4+8-4=8$.