alleryStart learning →Two non-zero vectors $\vec a$ and $\vec b$ are **collinear** (parallel) if and only if there exists a non-zero scalar $m$ such that:
- $\vec a + \vec b = 0$
- $\vec a = m\vec b$
- $|\vec a| = |\vec b|$
- $\vec a \cdot \vec b = 0$
Show answer and solution
Correct answer: B. $\vec a = m\vec b$
Collinearity ⇔ one is a scalar multiple of the other: $\vec a = m\vec b$ for some $m \ne 0$.
Magnitude equality alone doesn't imply collinearity, and the dot-product condition gives perpendicularity, not parallelism.