What is the unit vector in the direction of $\mathbf{a} = (5, -12)$?

$\left(\frac{5}{13}, -\frac{12}{13}\right)$

Two non-zero vectors $\mathbf{u}$ and $\mathbf{v}$ are perpendicular if and only if:

$\mathbf{u} \cdot \mathbf{v} = 0$

If the dot product $\mathbf{u} \cdot \mathbf{v}$ is negative for non-zero vectors $\mathbf{u}$ and $\mathbf{v}$, the angle between them is:

Obtuse (between $90^\circ$ and $180^\circ$)

Points $A$, $B$, $C$, $D$ have position vectors $\mathbf{a}$, $\mathbf{b}$, $\mathbf{c}$, $\mathbf{d}$. $ABCD$ is a parallelogram if and only if:

$\mathbf{a} + \mathbf{c} = \mathbf{b} + \mathbf{d}$

§-Quiz

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Vectors (HSC Maths Extension 1, 2026) quiz

10 questions. Pick an answer and you'll see why right away. Options are shuffled each attempt, and the review at the end links each missed question to the dot point to revise.

Given $\mathbf{u} = (3, 4)$ and $\mathbf{v} = (1, 2)$ , what is the scalar (dot) product $\mathbf{u} \cdot \mathbf{v}$ ?
What is the magnitude of the vector $\mathbf{a} = (5, -12)$ ?
What is the unit vector in the direction of $\mathbf{a} = (5, -12)$ ?
Two non-zero vectors $\mathbf{u}$ and $\mathbf{v}$ are perpendicular if and only if:
Find the value of $k$ such that $\mathbf{a} = (3, k)$ and $\mathbf{b} = (k - 2, 5)$ are perpendicular.
The vector projection of $\mathbf{a} = (4, 3)$ onto $\mathbf{b} = (2, -1)$ is:
Find the scalar projection of $\mathbf{a} = (6, 2)$ onto $\mathbf{b} = (3, 4)$ .
If $\mathbf{u} = 2\mathbf{i} - \mathbf{j}$ and $\mathbf{v} = \mathbf{i} + 3\mathbf{j}$ , what is $3\mathbf{u} - \mathbf{v}$ ?
If the dot product $\mathbf{u} \cdot \mathbf{v}$ is negative for non-zero vectors $\mathbf{u}$ and $\mathbf{v}$ , the angle between them is:
Points $A$ , $B$ , $C$ , $D$ have position vectors $\mathbf{a}$ , $\mathbf{b}$ , $\mathbf{c}$ , $\mathbf{d}$ . $ABCD$ is a parallelogram if and only if: