The 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.
Related questions
Three vectors $\vec a, \vec b, \vec c$ are coplanar if and only if:The cross product $\vec a\times\vec b$ of two parallel non-zero vectors is:The dot product $\vec a\cdot\vec b$ of $\vec a = 2\hat i - \hat j + 3\hat k$ and $\vec b =The magnitude of the vector $\vec a = 3\hat i + 4\hat j$ is:The magnitude of the vector $\hat{i}+\hat{j}+\hat{k}$ is:For any vector $\vec a$, the dot product $\vec a\cdot\vec a$ equals:The value of $\hat{i}\times\hat{j}$ is:The dot product of $(2\hat{i}+3\hat{j}+\hat{k})$ and $(\hat{i}-\hat{j}+\hat{k})$ is: