# Thread: Showing that two vectors are perpendicular

1. ## Showing that two vectors are perpendicular

Regarding the problem:

Show that for any vectors $\vec{a}$, $\vec{b}\in{R^3}$,
$\vec{u} = |\vec{b}|\vec{a} + |\vec{a}|\vec{b}$ and $\vec{v} = |\vec{b}|\vec{a} - |\vec{a}|\vec{b}$
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.

2. Originally Posted by gmer
Show that for any vectors $\vec{a}$, $\vec{b}\in{R^3}$,
$\vec{u} = |\vec{b}|\vec{a} + |\vec{a}|\vec{b}$ and $\vec{v} = |\vec{b}|\vec{a} - |\vec{a}|\vec{b}$
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.
What does $\vec{u}\cdot\vec{v}=~?$
Hint: Recall that $\vec{a}\cdot\vec{a}=\|a\|^2.$

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