3D Geometry
Line Intersection — |CD|²
nta_pyq_2026_jan
Grade 12
Question:
Let line $L_1$ be parallel to $-3\hat{i}+2\hat{j}+4\hat{k}$ and pass through $(2,6,7)$, and $L_2$ be parallel to $2\hat{i}+\hat{j}+3\hat{k}$ passing through $(4,3,5)$. If $L_3$ is parallel to $-3\hat{i}+5\hat{j}+16\hat{k}$ and intersects $L_1$ and $L_2$ at points $C$ and $D$, then $|\overrightarrow{CD}|^2$ is equal to:
Step-by-Step Solution
Key Concept: Find $\lambda_1,\lambda_2$ such that $D-C$ is parallel to $(-3,5,16)$. $C=(-3\lambda_1+2,2\lambda_1+6,4\lambda_1+7)$, $D=(2\lambda_2+4,\lambda_2+3,3\lambda_2+5)$.
$|\overrightarrow{CD}|^2=290$.
Correct Answer: 4