# Vector past paper question

• March 20th 2012, 05:28 PM
mathkid12
Vector past paper question
Given that the vector AB= 2i+3j and the vector CB= 5i + j

a. Show that AB is perpendicular to AC

You should know that \displaystyle \begin{align*} \mathbf{a} \cdot \mathbf{b} = |\mathbf{a}||\mathbf{b}|\cos{\theta} \end{align*}, where \displaystyle \begin{align*} \theta \end{align*} is the angle between \displaystyle \begin{align*} \mathbf{a} \end{align*} and \displaystyle \begin{align*} \mathbf{b} \end{align*}.
When \displaystyle \begin{align*} \theta = 90^{\circ} \end{align*} (i.e. when \displaystyle \begin{align*} \mathbf{a} \end{align*} and \displaystyle \begin{align*} \mathbf{b} \end{align*} are perpendicular), we have \displaystyle \begin{align*} \cos{\theta} = \cos{90^{\circ}} = 0 \end{align*}, which means that the dot product of the two vectors will also be 0.