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1. Jan 23, 2016

### lowea001

1. The problem statement, all variables and given/known data
Three ships A, B, and C move with velocities $\vec{v_{1}} \ \vec{v_{2}} \ \vec{u}$ respectively. The velocities of A and B relative to C are equal in magnitude and perpendicular. Show that $\left | \vec{u} -\frac{1}{2}(\vec{v_{1}} + \vec{v_{2}}) \right |^{2} = \left | \frac{1}{2}(\vec{v_{1}} - \vec{v_{2}}) \right |^{2}$

2. Relevant equations
Algebraic scalar product, vector product(?), magnitude of a vector.

3. The attempt at a solution

2. Jan 23, 2016

### PeroK

I can't see very well what you've done. Why not start with the condition that the relative velocities are perpendicular? What does that give you?

3. Jan 23, 2016

### SammyS

Staff Emeritus
The relative velocities are $\ \vec{v_1}-\vec{u} \$ and $\ \vec{v_2}-\vec{u} \$

NOT $\ \vec{v_1}+\vec{u} \$ and $\ \vec{v_2}+\vec{u} \$

4. Jan 23, 2016

### lowea001

I tried scalar product and equating to zero but as SammyS just noticed the problem seems to be in the initial statement that v1 + u is the relative velocity in the first place. Thank you!

5. Jan 23, 2016

### lowea001

Thank you very much.

6. Jan 23, 2016

### Staff: Mentor

Moved to Precalc section, as there is no calculus involved.