The problem involves proving that the sum of two linearly independent vectors of equal magnitude is perpendicular to their difference. The subject area is vector mathematics, specifically focusing on properties of vector addition and subtraction.
The discussion is ongoing, with participants seeking clarification on the definitions and relationships of the vectors involved. Some guidance has been offered regarding the notation and the implications of linear independence, but no consensus has been reached on a specific approach to the proof.
Participants note the requirement to show attempts at a solution in accordance with forum rules, which may influence the depth of responses provided.
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?noahsdev said: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.