Vector Algebra Question 12
Question 12 - 2024 (30 Jan Shift 2)
Let $\vec{a}$ and $\vec{b}$ be two vectors such that $|\vec{b}|=1$ and $|\vec{b} \times \vec{a}|=2$. Then $|(\vec{b} \times \vec{a})-\vec{b}|^{2}$ is equal to
(1) 3
(2) 5
(3) 1
(4) 4
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Answer (2)
Solution
$|\vec{b}|=1 &|\vec{b} \times \vec{a}|=2$
$(\vec{b} \times \vec{a}) \cdot \vec{b}=\vec{b} \cdot(\vec{b} \times \vec{a})=0$
$|(\vec{b} \times \vec{a})-\vec{b}|^{2}=|\vec{b} \times \vec{a}|^{2}+|\vec{b}|^{2}$
$=4+1=5$
