Way Too Many Crossproducts!

Geometry Level 3

Suppose \(\vec{p} , \vec{q}, \text{ and } \vec{r}\) are three mutually perpendicular unit vectors.

Vector \(\vec{u}\) satisfies the equation \[\vec{p}\times((\vec{u} - \vec{q})\times\vec{p}) \hspace{.15cm} + \hspace{.15cm} \vec{q}\times((\vec{u} - \vec{r})\times\vec{q}) \hspace{.15cm} + \hspace{.15cm}\vec{r}\times((\vec{u} - \vec{p})\times\vec{r}) = 0\]

What is \(\vec{u}\) in terms of \(\vec{p} , \vec{q}, \text{ and } \vec{r}\)?

×

Problem Loading...

Note Loading...

Set Loading...