# Thread: Vector past paper question

1. ## 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

2. ## Re: Vector past paper question

You should know that \displaystyle \displaystyle \begin{align*} \mathbf{a} \cdot \mathbf{b} = |\mathbf{a}||\mathbf{b}|\cos{\theta} \end{align*}, where \displaystyle \displaystyle \begin{align*} \theta \end{align*} is the angle between \displaystyle \displaystyle \begin{align*} \mathbf{a} \end{align*} and \displaystyle \displaystyle \begin{align*} \mathbf{b} \end{align*}.

When \displaystyle \displaystyle \begin{align*} \theta = 90^{\circ} \end{align*} (i.e. when \displaystyle \displaystyle \begin{align*} \mathbf{a} \end{align*} and \displaystyle \displaystyle \begin{align*} \mathbf{b} \end{align*} are perpendicular), we have \displaystyle \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.

Therefore, to show that two vectors are perpendicular, take the dot product and see if the dot product is 0.

3. ## Re: Vector past paper question

Of course, part of the problem is that you are not given vector "AC". You have to use the fact that AC= AB+ BC= AB- CB and then take the dot product of AC with AB.