The position vectors of points A and B are $\begin{pmatrix}-9\\3\end{pmatrix}$ and $\begin{pmatrix}1\\-12\end{pmatrix}$ respectively.

((a))
Find the column vector $\overrightarrow{BA}$ .
((b))
Find $|\overrightarrow{BA}|$ .

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Worked solution

6((a))

1. Use position vectors to find the vector from $B$ to $A$.

$\overrightarrow{BA}=\vec{OA}-\vec{OB}$
$=\begin{pmatrix}-9\\3\end{pmatrix}-\begin{pmatrix}1\\-12\end{pmatrix}$
$=\begin{pmatrix}-9-1\\3-(-12)\end{pmatrix}$
$=\begin{pmatrix}-10\\15\end{pmatrix}$

Answer

$\overrightarrow{BA}=\begin{pmatrix}-10\\15\end{pmatrix}$

6((b))

1. Substitute the components of $\overrightarrow{BA}$ into the magnitude formula.

From part (a),
$\overrightarrow{BA}=\begin{pmatrix}-10\\15\end{pmatrix}.$
Hence
$|\overrightarrow{BA}|=\sqrt{(-10)^2+15^2}.$

2. Evaluate and simplify the square root.

$|\overrightarrow{BA}|=\sqrt{100+225}$
$=\sqrt{325}$
$=5\sqrt{13}.$

Answer

$|\overrightarrow{BA}|=5\sqrt{13}$

AI analysis — may contain mistakes.

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The position vectors of points A and B are (−93)\begin{pmatrix}-9\\3\end{pmatrix}(−93​) and (1−12)\begin{pmatrix}1\\-12\end{pmatrix}(1−12​) respectively.

Worked solution

6((a))

6((b))

More questions on this topic

The position vectors of points A and B are $\begin{pmatrix}-9\\3\end{pmatrix}$ and $\begin{pmatrix}1\\-12\end{pmatrix}$ respectively.