If OC + OA = 2OB, prove that A, B, and C are colinear and B is the midpoint of AC.

Question

If OC + OA = 2OB, prove that A, B, and C are colinear and B is the midpoint of AC.
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Solution 1

Sure, here is the step by step proof:

  1. Given that OC + OA = 2OB, we can rearrange this equation to OA + OC - 2OB = 0.

  2. This can be further simplified to OA - OB + OC - OB = 0.

  3. Now, we can rewrite this equation in terms of vectors: OA - OB = OB - OC.

  4. This equation tells us that the vect 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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