3D Geometry
Line Through Origin Perpendicular to Two Lines
nta_pyq_2023_apr
Grade 12
Question:
$L$ through origin $\perp L_1$ and $L_2$. $P$ = intersection of $L$ and $L_1$. $Q(\alpha,\beta,\gamma)$ = foot of $\perp$ from $P$ on $L_2$. Then $9(\alpha+\beta+\gamma)$ is equal to ________.
Step-by-Step Solution
Key Concept: Direction of $L=\vec{d}_1\times\vec{d}_2=(1,2,3)\times(2,2,1)=(-4,5,-2)$. Find $P$ on $L_1$, then foot $Q$ on $L_2$.
$9(\alpha+\beta+\gamma)=5$.
Correct Answer: 5