Dot Product of Like Vectors/Mistake

Source Work

 * Chapter $\text {II}$: The Products of Vectors
 * $2$. The Scalar Product: $(2.3)$
 * $2$. The Scalar Product: $(2.3)$

Mistake

 * When two vectors are perpendicular, therefore,
 * $\mathbf A \cdot \mathbf B = 0$, $\qquad (2.2)$
 * and when they are parallel,
 * $\mathbf A \cdot \mathbf B = A B$. $\qquad (2.3)$

Correction
Being parallel is insufficient.

Parallel vector quantities may have opposite directions, that is, such that $\theta = 180 \degrees$, in which case $\mathbf A \cdot \mathbf B = -A B$.

For $\mathbf A \cdot \mathbf B = AB$, it is necessary for $\mathbf A$ and $\mathbf B$ to be like, that is, for their directions to be equal.