Homework Help: Advanced Vector Problem: Ships

Tags:
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.