Vectors (HSC Maths Extension 1, 2026) quiz

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: