Given that the vector AB= 2i+3j and the vector CB= 5i + j
a. Show that AB is perpendicular to AC
how to do this????.... have no clue on how to start please help
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.