Prove that the sum and difference of equal-magnitude vectors are perpendicular

[noahsdev]

Homework Statement

If two linearly independent vectors are of equal magnitude, prove that their sum is perpendicular to their difference.

Homework Equations

v1.v2 = 0

The Attempt at a Solution

This question doesn't seem that hard but it's really confused me.
Help is appreciated, thanks.

 

[vanhees71]

Just write down the scalar product!

 

[HallsofIvy]

Homework Statement

If two linearly independent vectors are of equal magnitude, prove that their sum is perpendicular to their difference.

Homework Equations

v1.v2 = 0

This is a "relevant equation" only if you say what v1 and v2 are! In particular are you clear that v1 and v2 are NOT the "two linearly independent vectors" of the question? Call the two vectors u and v. Their sum is u+ v and their difference is u- v. So "their sum is perpendicular to their difference" means (u+ v).(u- v)= 0. What does the fact that they are linearly independent tell you?

The Attempt at a Solution

This question doesn't seem that hard but it's really confused me.
Help is appreciated, thanks.

 

[Mark44]

noahsdev, per Physics Forums rules, you must show what you have tried when you post a question.