What does this vector equal to?

[Cuisine123]

Homework Statement

Prove that |\vec{A}|²+|\vec{B}|² equals to \frac{1}{2}(|\vec{A}+\vec {B}|²+|\vec{A}-\vec{B}|²)

Homework Equations

Perhaps the triangle inequality? I am not sure.

The Attempt at a Solution

I have no idea how to approach this question. Please help me with clear explanations. Thank you.

 

[tiny-tim]

Hi Cuisine123!

Use the definition of modulus: |A + B|² = (A + B).(A + B) etc

 

[D H]

Perhaps not the triangle inequality. That is an inequality. You are looking for an equality.

Have you tried expanding the right hand side?