The vector dot product is a crucial function in vector algebra, with significant implications in the fields of computer science and physics. This operation is performed by multiplying the matching entries of the two vectors involved and then summing the resulting products. The output is a scalar. Alternatively, it can be determined using the vectors' magnitude and the cosine of the angle separating them.
| Topic | Problem | Solution |
|---|---|---|
| None | Find $\mathbf{u} \cdot \mathbf{v}$, where $\theta… | We are given the magnitudes of vectors \(\mathbf{u}\) and \(\mathbf{v}\) as 7 and 8 respectively, a… |
| None | Find the dot product, \( \vec{u} \cdot \vec{w} \)… | \( \vec{u} \cdot \vec{w} = (-7)(4) + (-4)(-3) \) |
| None | Find the dot product, \( \vec{u} \cdot \vec{w} \)… | \( \vec{u} \cdot \vec{w} = 5\times12 + 3\times4 \) |