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WZ
Numerade Educator

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Problem 58 Hard Difficulty

If $ c = \mid a \mid b + \mid b \mid a $, where $ a $, $ b $, and c are all nonzero vectors, show that $ c $ bisects the angle between $ a $ and $ b $.

Answer

$\alpha=\beta$

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Video Transcript

The problem is, if C is equal to the magnitude of a Times B plus magnitude B times a while, ABC are all non zero. Lectures showed that c bisects the angle between A and B. This problem what we need to do is to prove the angle between but to A and C is equal to the angle between B and C. So here, with the note angle between a and the sea at each one angle between B and the C is set to then we have the definition consign data one. This is equal to see Dr P over, uh, magnitude of three times magnitude of A. This is equal to magnitude of eight times B plus magnitude of B times A Not to pay unfair. I need you to three times my intuitive for a this is equal to magnitude of a and speed dot a plus magnitude to be times magnitude of a square over nine to see has my interest of a This is equal to be a doctor a last magnitude of B times magnitude of a over magnitude of C. The CAS, unfit to is equal to see that be over magnitude of C has mind you to be. This is equal to the same thing here that be over. See magnitude up. See, hence magnitude of P. This is echo two magnitude of eight times magnitude of the Squire plus magnitude B times a dot be over magnitude of C times. Magnitude be This is equal to magnitude of eight times magnitude of B as a dot be over magnitude of C since eight dot be is equal to be dot a behalf. Because I am fit. One is equal to the same fate too. So we have that one is equal to two. So I want to see by sex angle between A and B.