The dot product formula is a useful tool for determining the angle between two vectors. According to this formula, the dot product of two vectors is equivalent to the multiplication of their magnitudes and the cosine of the angle that separates them. With some manipulation of this formula, we are able to isolate and solve for the angle between the vectors.
| Topic | Problem | Solution |
|---|---|---|
| None | Given $\mathbf{v}=-7 \mathbf{i}-6 \mathbf{j}$ and… | Given vectors \(\mathbf{v}=-7 \mathbf{i}-6 \mathbf{j}\) and \(\mathbf{w}=5 \mathbf{i}-\mathbf{j}\),… |
| None | Find the angle, \( \alpha \), between the vectors… | \(\cos\alpha = \frac{\overrightarrow{u} \cdot \overrightarrow{w}}{||\overrightarrow{u}|| ||\overrig… |
| None | Find the angle between $2 \mathbf{i}+5 \mathbf{j}… | Given vectors \(\mathbf{A} = 2 \mathbf{i}+5 \mathbf{j}\) and \(\mathbf{B} = \mathbf{j}\). |
| None | Find the angle $\theta$ (in degrees) between the … | We are given the vectors \(\mathbf{u} = 3\mathbf{i} - 6\mathbf{j}\) and \(\mathbf{v} = 9\mathbf{i} … |
| None | Given the vectors $\vec{u}=7 i+10 j$ and $\vec{v}… | Given the vectors \(\vec{u}=7 i+10 j\) and \(\vec{v}=3 i+2 j\), we are to find the angle (in degree… |