Vector Algebra
Triple Product — Scalar Dot of Cross Products
nta_pyq_2026_jan
Grade 12
Question:
Let $\vec{a}=-\hat{i}+\hat{j}+2\hat{k}$, $\vec{b}=\hat{i}-\hat{j}-3\hat{k}$, $\vec{c}=\vec{a}\times\vec{b}$ and $\vec{d}=\vec{c}\times\vec{a}$. Then $(\vec{a}-\vec{b})\cdot\vec{d}$ is equal to:
Step-by-Step Solution
Key Concept: $\vec{c}=\vec{a}\times\vec{b}=(-1,-1,0)$. $\vec{d}=\vec{c}\times\vec{a}=(-2,2,-2)$. $\vec{a}-\vec{b}=(-2,2,5)$.
$(\vec{a}-\vec{b})\cdot\vec{d}=-2$.
Correct Answer: 4