Question

Given that magnitude of A= magnitude of B. What is the angle between (A+B) and (A-B) ?

Answer 1

@hartnn

Answer 2

Sorry m big noob in mathematics

Answer 3

Ok i know geometrically, it will be 90°. Can u help me finding in a numerical way ?

Answer 4

yes
know the formula for dot product ?

Answer 5

yep

Answer 6

A.B= ABCos\(\theta\)

Answer 7

so, cos theta = x.y /(|x||y|)

right ??

i took x and y because A,B would be confusing

x= A+B, y =A-B

Answer 8

ok..

Answer 9

just try to find the numerator of cos theta

(A+B). (A-B) = .... ?

Answer 10

A\(^2\) + B\(^2\) + 2ABCos\(\theta\) ..... like this ?

Answer 11

no...
foil it
(A+B).(A-B) = ... ?

(like z(x+y) = xz +yz)

Answer 12

first term will be
\(A.A = A (dot)A = |A|^2 \)

Answer 13

don't forget the dots...its a dot product operation

A.B -B.A = A.B -A.B = 0
(because dot product is commutitive)

Answer 14

oh..yes..i got it !

Answer 15

so, numerator is |A|^2 -|B|^2
and it is given that |A| = |B|

when is cos theta = 0 ?

Answer 16

90

Answer 17

great !

Answer 18

\(\huge \checkmark \)

Answer 19

Thnx once again !!
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