# How do you find the angle between the vectors u=5i+5j and v=-8i+8j?

Jul 14, 2016

Angle: 90°

#### Explanation:

In order to calculate the angle between two vectors, we have to know that

$\cos \left(\theta\right) = \frac{\vec{u} \cdot \vec{v}}{| | \vec{u} | | | | \vec{v} | |}$

$u \cdot v$ means the dot product of $u$ and $v$, which we can calculate using the formula

$\vec{u} \cdot \vec{v} = {u}_{1} {v}_{1} + {u}_{2} {v}_{2} + \ldots {u}_{n} {v}_{n}$

In our case, $\vec{u} = 5 \hat{i} + 5 \hat{j}$ and $\vec{v} = - 8 \hat{i} + 8 \hat{j}$

$\vec{u} \cdot \vec{v} = 5 \left(- 8\right) + 5 \left(8\right) = - 40 + 40 = 0$

Since the dot product is $0$, we can conclude that $\vec{u}$ and $\vec{v}$ are perpendicular to each other, so the angle between them would equal $90$.