3D Geometry
Equation of plane through a point parallel to two lines
Grade Class 12
Question:
If the equation of the plane through $(-1,2,0)$ and parallel to lines $\dfrac{x}{3}=\dfrac{y+1}{0}=\dfrac{z-2}{-1}$ and $\dfrac{x-1}{1}=\dfrac{y+1}{2}=\dfrac{z+1}{-1}$ is $ax+by+cz=1$, then $a+b+c$ is
Step-by-Step Solution
Key Concept: Normal to the plane is perpendicular to both direction vectors $(3,0,-1)$ and $(1,2,-1)$. Compute normal as their cross product.
Normal $(1,1,3)$. Plane $x+y+3z=1$. $a+b+c=5$.
Correct Answer: 3