3D Geometry
Plane Containing Line and Perpendicular to Given Plane
nta_pyq_2023_apr
Grade 12
Question:
Plane containing $x+2y+3z-4=0=2x+y-z+5$ and $\perp$ to $\vec{r}=(\hat{i}-\hat{j})+\lambda(\hat{i}+\hat{j}+\hat{k})+\mu(\hat{i}-2\hat{j}+3\hat{k})$ is $ax+by+cz=4$. Then $a-b+c$ is equal to
Step-by-Step Solution
Key Concept: Plane through line of intersection: family $P_1+\lambda P_2=0$. Normal perpendicular to both direction vectors of given plane.
$a-b+c=22$.
Correct Answer: 2