Advanced Vector Problem: Ships

[lowea001]

Homework Statement

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}

Homework Equations

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

The Attempt at a Solution

[/B]

 

[PeroK]

Homework Statement

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}

Homework Equations

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

The Attempt at a Solution

View attachment 94694 [/B]

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?

 

[SammyS]

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} \$

 

[lowea001]

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?

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!

 

[lowea001]

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} \$

Thank you very much.

 

[Mark44]

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