Vector Algebra
Dot product of derived vector
nta_pyq_2023_jan
Grade 12
Question:
Let $\vec{a}$ and $\vec{b}$ be two vectors. Let $|\vec{a}|=1$, $|\vec{b}|=4$ and $\vec{a}\cdot\vec{b}=2$. If $\vec{c} = (2\vec{a}\times\vec{b})-3\vec{b}$, then the value of $\vec{b}\cdot\vec{c}$ is
Step-by-Step Solution
Key Concept: Compute $\vec{b}\cdot\vec{c} = \vec{b}\cdot(2\vec{a}\times\vec{b}) - 3|\vec{b}|^2$. The first term is zero (scalar triple product with repeated vector).
$\vec{b}\cdot\vec{c} = 0 - 3|\vec{b}|^2 = -48$. Answer: (2)
Correct Answer: $-48$