3D Geometry
Plane Through Line of Intersection, Parallel to Line
nta_pyq_2023_apr
Grade 12
Question:
Plane through intersection of $2x-y+z=3$ and $4x-3y+5z+9=0$, parallel to $\frac{x+1}{-2}=\frac{y+3}{4}=\frac{z-2}{5}$, is $ax+by+cz+6=0$. Then $a+b+c$ is
Step-by-Step Solution
Key Concept: Family: $(2x-y+z-3)+\lambda(4x-3y+5z+9)=0$. Normal perpendicular to line direction $(-2,4,5)$ gives $\lambda$.
$a+b+c=14$.
Correct Answer: 2