3D Geometry
Projection of Vector on Perpendicular to Two Vectors
nta_pyq_2023_apr
Grade 12
Question:
$O$ origin, $P=-\hat{i}-2\hat{j}+3\hat{k}$. $A=-2\hat{i}+\hat{j}-3\hat{k}$, $B=2\hat{i}+4\hat{j}-2\hat{k}$, $C=-4\hat{i}+2\hat{j}-\hat{k}$. Projection of $\overrightarrow{OP}$ on vector $\perp\overrightarrow{AB}$ and $\overrightarrow{AC}$ is
$\dfrac{3}{8}$
$\dfrac{8}{3}$
$\dfrac{7}{3}$
$\dfrac{3}{10}$
Step-by-Step Solution
Key Concept: $\vec{n}=\overrightarrow{AB}\times\overrightarrow{AC}$. Projection $=\frac{\overrightarrow{OP}\cdot\hat{n}}{|\hat{n}|}=\frac{\overrightarrow{OP}\cdot\vec{n}}{|\vec{n}|}$.
Projection $=\frac{3}{8}$.
Correct Answer: 1