Vector Algebra
Vector Cross Product — Magnitude Expression
nta_pyq_2023_apr
Grade 12
Question:
$\vec{a}=3\hat{i}+\hat{j}-\hat{k}$, $\vec{c}=2\hat{i}-3\hat{j}+3\hat{k}$. $\vec{a}=\vec{b}\times\vec{c}$, $|\vec{b}|^2=50$. Then $|72-|\vec{b}+\vec{c}|^2|$ is equal to __________.
Step-by-Step Solution
Key Concept: $\vec{b}\times\vec{c}=\vec{a}$. $\vec{b}\cdot\vec{c}\cdot\sin\theta=|\vec{a}|$... find $\vec{b}$ component parallel to $\vec{c}$. Use $|\vec{b}+\vec{c}|^2=|\vec{b}|^2+|\vec{c}|^2+2\vec{b}\cdot\vec{c}$.
$66$.
Correct Answer: 66