Step by Step Solver to Find the Angle Between two Vectors

1) The angle $\theta$ between two vectors $\vec{u}$ and $\vec{v}$ is given by: $\theta= \arccos(\dfrac{\vec{u}\cdot \vec{v}}{||\vec{u}|| \cdot ||\vec{v}||})$

2) The magnitude $||\vec{u}||$ of a vector $ \vec{u} $ given by its components as $\vec{u} = \langle a, b \rangle $ is given by $||\vec{u}||=\sqrt{a^2+b^2}$

3) If $\vec{u} = \langle a, b \rangle $ and $\vec{v} = \langle c, d \rangle $ , the dot product $\vec{u}\cdot \vec{v} = a \cdot c + b \cdot d$

Solve each step below then click on "Show me" to check your answer. There is a graph at the bottom of the page that helps you further understand graphically the solution to the question shown below.

Step by step solution

Below are shown the two vectors, $\vec u$ (green) $\vec v$ (blue) and angle $\theta, \text{such that } 0\le \theta \le 180^{\circ}$, (red) between them.

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