When you multiply a vector by a scalar, what you're essentially doing is multiplying each individual component of the vector by that scalar. The outcome of this operation is a new, scaled vector that aligns parallel to the initial vector, with its magnitude being adjusted by the scalar. Take note, if the scalar used is negative, the direction of the resulting vector will be inversed.
| Topic | Problem | Solution |
|---|---|---|
| None | For $\mathbf{u}=\langle 3,-1\rangle, \mathbf{v}=\… | Given vectors are \(\mathbf{u} = \langle 3,-1 \rangle\), \(\mathbf{v} = \langle 3,1 \rangle\), and … |