3D Geometry
Distance Parallel to SD Line Direction
nta_pyq_2023_apr
Grade 12
Question:
Distance of $(-1,2,3)$ from $\vec{r}\cdot(\hat{i}-2\hat{j}+3\hat{k})=10$ measured $\parallel$ to SD line between $\vec{r}=(\hat{i}-\hat{j})+\lambda(2\hat{i}+\hat{k})$ and $\vec{r}=(2\hat{i}-\hat{j})+\mu(\hat{i}-\hat{j}+\hat{k})$ is
$4\sqrt{6}$
$2\sqrt{5}$
$2\sqrt{6}$
$3\sqrt{5}$
Step-by-Step Solution
Key Concept: Find SD direction $=\vec{d}_1\times\vec{d}_2=(2,0,1)\times(1,-1,1)=(1,-1,-2)$. Line through $(-1,2,3)$ in this direction, meet given plane.
$2\sqrt{6}$.
Correct Answer: 3