When are these vectors parallel/perpendicular/the same length?

Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Given the vectors \(\mathbf{U}=\begin{pmatrix}7 \\ 6\end{pmatrix}\) and \(\mathbf{V}=\begin{pmatrix}2 \\ x\end{pmatrix}\), find the value or values of \(x\) for which

1. \(\mathbf{U}\) is parallel to \(\mathbf{V}\),
2. \(\mathbf{U}\) is perpendicular to \(\mathbf{V}\),
3. \(\mathbf{U}\) and \(\mathbf{V}\) have the same magnitude.