Vector Algebra
Parallel Vectors from Cross Product Condition
nta_pyq_2023_apr
Grade 12
Question:
Let $\vec{a}\times\vec{c}=\vec{a}\times\vec{b}$. If $\vec{a}\cdot\vec{c}=-12$, $\vec{c}\cdot(\hat{i}-2\hat{j}+\hat{k})=5$, then $\vec{c}\cdot(\hat{i}+\hat{j}+\hat{k})$ is equal to _______
Step-by-Step Solution
Key Concept: $\vec{a}\times(\vec{c}-\vec{b})=0\Rightarrow\vec{c}=\vec{b}+\lambda\vec{a}$. Use $\vec{a}\cdot\vec{c}=-12$ and second condition to find $\lambda$ and $\vec{c}$.
$\vec{c}\cdot(\hat{i}+\hat{j}+\hat{k})=11$.
Correct Answer: 11