The discussion centers on proving that the sum of two linearly independent vectors of equal magnitude is perpendicular to their difference. The vectors are denoted as u and v, leading to the equation (u + v) · (u - v) = 0. This equation confirms the perpendicularity condition, as the scalar product must equal zero. The importance of linear independence in this context is emphasized, as it ensures that the vectors are not collinear.
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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.