Regarding the problem:
Show that for any vectors \(\displaystyle \vec{a}\), \(\displaystyle \vec{b}\in{R^3}\),
\(\displaystyle \vec{u} = |\vec{b}|\vec{a} + |\vec{a}|\vec{b}\) and \(\displaystyle \vec{v} = |\vec{b}|\vec{a} - |\vec{a}|\vec{b}\)
are perpendicular
I'm not exactly sure where to begin with this problem. I think maybe taking the dot product of u and v but I'm not sure.
Show that for any vectors \(\displaystyle \vec{a}\), \(\displaystyle \vec{b}\in{R^3}\),
\(\displaystyle \vec{u} = |\vec{b}|\vec{a} + |\vec{a}|\vec{b}\) and \(\displaystyle \vec{v} = |\vec{b}|\vec{a} - |\vec{a}|\vec{b}\)
are perpendicular
I'm not exactly sure where to begin with this problem. I think maybe taking the dot product of u and v but I'm not sure.