Question:

Plane through $(-2,3,5)$, $\perp$ to $2x+4y+5z=8$ and $3x-2y+3z=5$: $\alpha x+\beta y+\gamma z+97=0$. Then $\alpha+\beta+\gamma$ is

Step-by-Step Solution

Key Concept: Normal = $\vec{n}_1\times\vec{n}_2=(4\cdot3-5\cdot(-2),5\cdot3-2\cdot3,2\cdot(-2)-4\cdot3)=(22,9,-16)$.

$\alpha+\beta+\gamma=15$.

Correct Answer: 1