Show that the vectors u = (2, -3) and v = (–4, 6) are parallel.
Show that the vectors u = (2, -3) and v = (–4, 6) are parallel.
\cos \varphi=\frac{\mathbf{u} \cdot \mathbf{v}}{|\mathbf{u}||\mathbf{v}|}=\frac{-8-18}{\sqrt{13} \sqrt{52}}=\frac{-26}{\sqrt{13}(2 \sqrt{13})}=\frac{-26}{2(13)}=-1,
so φ = π.