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 2 years ago
Hi there, Im having troube with understanding the solution to the example 5 in cartesiancoordinatesandvector course notes:"Show that if /A  B/ = /A + B/ , then A is perpendicular to B.". I dont see how if /A  B/ = ((A.A  2A.B + B.B))
and if /A + B/ = ((A + B)!(A + B)) = ((A.A + 2A.B + B.B) would imply that A.B=0. Cheers!
 2 years ago
Hi there, Im having troube with understanding the solution to the example 5 in cartesiancoordinatesandvector course notes:"Show that if /A  B/ = /A + B/ , then A is perpendicular to B.". I dont see how if /A  B/ = ((A.A  2A.B + B.B)) and if /A + B/ = ((A + B)!(A + B)) = ((A.A + 2A.B + B.B) would imply that A.B=0. Cheers!

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runriot
 2 years ago
Best ResponseYou've already chosen the best response.0first its AB^2 = A.A 2A.B + B.B and similarly for A+B but that's not the essential idea here. What is essential is that if AB = A+B then A.A 2A.B + B.B = A.A + 2A.B + B.B => that A.B = A.B which can only mean that A.B=0 therefore A perp to B
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