*(Vector algebra --- not a differential equation; included as extracted.)* Let a, b, c be …

Question

*(Vector algebra --- not a differential equation; included as extracted.)*

Let $\vec a,\vec b,\vec c$ be mutually perpendicular, same magnitude. If $\vec r$ satisfies

$$\vec a\times[(\vec r-\vec b)\times\vec a]+\vec b\times[(\vec r-\vec c)\times\vec b]+\vec c\times[(\vec r-\vec a)\times\vec c]=0,$$
then $\vec r$ equals:

Accepted Answer

Expanding via the BAC-CAB rule and using orthogonality and equal magnitudes gives $3\vec r-(\vec a+\vec b+\vec c)-\vec r=0 \implies \vec r=\dfrac{\vec a+\vec b+\vec c}{2}$.

Solutions · 1