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If the angle between vectors $\vec A$ and $\vec B$ is $90^\circ$, then
A$\vec A\cdot\vec B = AB$
B$\vec A\cdot\vec B = 0$
C$|\vec A\times\vec B| = 0$
D$\vec A\times\vec B$ is parallel to $\vec A$
Answer & Solution
Correct answer: B. $\vec A\cdot\vec B = 0$
The dot product is $\vec A\cdot\vec B = AB\cos\theta$. For $\theta=90^\circ$, $\cos 90^\circ=0$, so the dot product is zero. In contrast, the cross-product magnitude is maximum at right angles and equals $AB$.
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