IGCSE Math B 8.F Vector magnitude Topic Practice

ABC is a triangle.
$$\overrightarrow{AB}=\begin{pmatrix}3\\-2\end{pmatrix}, \qquad \overrightarrow{BC}=\begin{pmatrix}x\\5x\end{pmatrix}, \qquad x>0, \qquad |\overrightarrow{AC}|=5.$$
Find $\overrightarrow{AC}$ as a column vector.
Show clear algebraic working.

$\overrightarrow{O X}=\binom{-4}{2}$ and $\overrightarrow{Y X}=\binom{-7}{6}$

Calculate the modulus of $\overrightarrow{O Y}$

The position vector of A is $\binom{-3}{8}$.
The point B has coordinates (2,-4).
Find $|\overrightarrow{AB}|$.

The vectors
$$\mathbf p=\begin{pmatrix}x\\2x-1\end{pmatrix}, \qquad \mathbf q=\begin{pmatrix}-9\\5\end{pmatrix}$$
are such that $|\mathbf p|=|\mathbf q|$.
Given that x<0, find the value of x.

Given that
$$\mathbf a=\binom{x-2}{\sqrt{2x}}$$
where $|\mathbf a|=\sqrt5$, find the exact value of x.

The coordinates of point A are (1,8) and the coordinates of point B are (10,-4).

Calculate the modulus of A P.

$21 \overrightarrow{O X}=\binom{2}{5}$ and $\overrightarrow{O Y}=\binom{-2}{7}$

Calculate $|\overrightarrow{X Y}|$, giving your answer as a surd.

The vectors
$$\mathbf p=\begin{pmatrix}2x-1\\y\end{pmatrix}, \qquad \mathbf q=\begin{pmatrix}y+3\\-y\end{pmatrix}$$
are such that $|\mathbf p|=\sqrt{98}$ and
$$\mathbf p+\mathbf q=\begin{pmatrix}7\\0\end{pmatrix}.$$

Figure 4 shows a trapezium OACB in which $\angle O A C=\angle A O B=90^{\circ}$ so that OB and AC are parallel.
Given that $\overrightarrow{O A}=\mathbf{a}, \overrightarrow{O B}=\mathbf{b}$ and $\overrightarrow{A C}=2 \mathbf{b}$,

Given that $|\mathbf{a}|=6$ cm and $|\mathbf{b}|=8$ cm,

calculate the length, in cm to 3 significant figures, of OP.