3D Geometry
Plane Through Line of Intersection, Through Point
nta_pyq_2023_apr
Grade 12
Question:
Plane $P$ contains line of intersection of $\vec{r}\cdot(\hat{i}+\hat{j}+\hat{k})=6$ and $\vec{r}\cdot(2\hat{i}+3\hat{j}+4\hat{k})=-5$. $P$ passes through $(0,2,-2)$. Square of distance from $(12,12,18)$ to $P$ is
Step-by-Step Solution
Key Concept: Family plane: $(x+y+z-6)+\lambda(2x+3y+4z+5)=0$. Substitute $(0,2,-2)$ to find $\lambda$.
Distance$^2=620$.
Correct Answer: 1