AHL 3.10—Vector definitions

A vector has both magnitude and direction, while a scalar has magnitude only.

Option A states 'magnitude only, no direction', which matches the definition of a scalar exactly.

The correct answer is A.

This describes a vector, not a scalar, since it includes direction.

Pointing along an axis is a property some vectors have, not a defining feature of scalars.

Scalars can be negative (e.g. temperature can be -5°C), so this is not the defining property.

$\overrightarrow{AB}=\mathbf{b}-\mathbf{a}$, destination minus source.

$\overrightarrow{AB}=\left(\begin{array}{c}5-2\\ 1-(-3)\\ -2-1\end{array}\right)=\left(\begin{array}{c}3\\ 4\\ -3\end{array}\right)$.

This matches option A.

This is $\overrightarrow{BA}=\mathbf{a}-\mathbf{b}$, the reverse displacement, not $\overrightarrow{AB}$.

This results from adding components instead of subtracting.

This has the correct first and third components but the second component sign is wrong: $1-(-3)=4$, not $-4$.