Vector Algebra
Vector Triple Product — Finding $24-\vec{b}\cdot\vec{c}$
nta_pyq_2024_apr
Grade 12
Question:
Let $\vec{a}=2\hat{i}-3\hat{j}+4\hat{k}$, $\vec{b}=3\hat{i}+4\hat{j}-5\hat{k}$ and a vector $\vec{c}$ be such that $\vec{a}\times(\vec{b}+\vec{c})+\vec{b}\times\vec{c}=\hat{i}+8\hat{j}+13\hat{k}$. If $\vec{a}\cdot\vec{c}=13$, then $(24-\vec{b}\cdot\vec{c})$ is equal to _____
Step-by-Step Solution
Key Concept: $\vec{a}\times\vec{b}+\vec{a}\times\vec{c}+\vec{b}\times\vec{c}=\hat{i}+8\hat{j}+13\hat{k}$. Take dot product of $\vec{a}$ with $\vec{a}\times(\text{above})$ and use BAC-CAB rule repeatedly.
$\vec{b}\cdot\vec{c}=-22$. $24-\vec{b}\cdot\vec{c}=46$.
Correct Answer: 46