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:
A$\vec a + \vec b = 0$
B$\vec a = m\vec b$
C$|\vec a| = |\vec b|$
D$\vec a \cdot \vec b = 0$
Answer & 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.
Related questions
Vector $PQ$ has magnitude 5 units and is inclined at $150^{\circ}$ to the $x$-axis. In theForces $2i-5j+6k$ and $-i-2j-k$ move a particle from $A(4,-3,-2)$ to $B(6,-1,-3)$. The worPosition vectors $2i-j+k$, $i-3j-5k$ and $3i-4j-4k$ form a triangle with sides $ qrt{41}$,When are two vectors counted as equal?What is the magnitude of the position vector with components 9 and 12?Which two features identify a vector?The work done by a constant force F in displacement d isIf a, b, c are mutually perpendicular unit vectors, the value of a · (b × c) is