alleryThe dot product (scalar product) of two vectors $\vec{a}$ and $\vec{b}$ is:
A$|\vec{a}||\vec{b}|\cos\theta$
B$|\vec{a}|^2 + |\vec{b}|^2$
C$|\vec{a}||\vec{b}|\sin\theta$
D$|\vec{a}||\vec{b}|\tan\theta$
Answer & Solution
Correct answer: A. $|\vec{a}||\vec{b}|\cos\theta$
The dot product is defined as $\vec{a} \cdot \vec{b} = |\vec{a}||\vec{b}|\cos\theta$ where $\theta$ is the angle between them. The result is a scalar.
The sine version (option A) defines the magnitude of the cross product, which is a vector, not a scalar. Mixing up the two is a recurring exam trap.
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