Vector Algebra
Cross Product
Grade None
Question:
<p>[JEE Main 2022] Let \(\vec{a}=\hat{i}+\hat{j}+\hat{k}\) and \(\vec{b}=2\hat{i}+\hat{j}-\hat{k}\). If \(\vec{p}\) is such that \(\vec{a}\times\vec{p}=\vec{b}\) and \(\vec{a}\cdot\vec{p}=0\), then the value of \([\vec{a},\vec{p},\vec{b}]\) is</p>
\(6\)
\(-6\)
\(3\sqrt3\)
\(-3\sqrt3\)
Step-by-Step Solution
Key Concept: [a,p,b]=(a \times p) \cdot b=b \cdot b=|b|^2. Compute |b|^2=4+1+1=6.
$[\vec{a},\vec{p},\vec{b}]=(\vec{a}\times\vec{p})\cdot\vec{b}=\vec{b}\cdot\vec{b}=|\vec{b}|^2=4+1+1=6$. Answer: (A)
Correct Answer: A