Let x and y be two vectors from Rn. Show that x − y andx + y are orthogonal if and only if ∥x∥ = ∥y∥

Question

Let x and y be two vectors from Rn. Show that x − y andx + y are orthogonal if and only if ∥x∥ = ∥y∥
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Solution 1

Sure, let's go through this step by step.

Two vectors are orthogonal if their dot product is zero. So, we need to show that (x - y) and (x + y) are orthogonal, i.e., their dot product is zero, if and only if ∥x∥ = ∥y∥.

Step 1: Assume ∥x∥ = ∥y∥. We need to show that (x - y) and (x + y) are orthogon Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

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