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?