Question 78

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

$$|\vec{b}| = 1$$, $$|\vec{b} \times \vec{a}| = 2$$.

$$|(\vec{b} \times \vec{a}) - \vec{b}|^2 = |\vec{b} \times \vec{a}|^2 - 2(\vec{b} \times \vec{a}) \cdot \vec{b} + |\vec{b}|^2$$

Since $$(\vec{b} \times \vec{a}) \perp \vec{b}$$: $$(\vec{b} \times \vec{a}) \cdot \vec{b} = 0$$.

$$= 4 + 0 + 1 = 5$$.

The answer is Option (2): $$\boxed{5}$$.

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