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Can the sum of the magnitude of two vectors ever be equal to the magnitude of the sum of these two vectors???

Can the sum of the magnitude of two vectors ever be equal to the magnitude of the sum of these two vectors???
 
 

Grade:12th pass

2 Answers

Anirudh
15 Points
6 years ago
Mathematically,Let the vectors be a and b with magnitudes a and b respectively and the angle between them be x.Magnitude of the sum of a and b is√(a^2+b^2+2abcosxDifference in their magnitudes isa-bHence,√(a^2+ b^2+2ab cosx) = a-bSquaring both sides,a^2+b^2+2ab cos x = a^2+ b^2–2ab2ab cosx+2ab =02ab(cosx +1) =0Since 2ab can`t be zero,Cos x+1=0Cosx=-1X=180
Khimraj
3007 Points
6 years ago
Yes. this is posible but only when angle between these two vecor is zero.
Proof:-
Let first vector has magnitude A and second vector has magnitude B. And angle between these two is \Theta.
Then
A+B = (A2+B2+2ABcos\Theta)½
(A+B)2 = (A2+B2+2ABcos\Theta)
A2+B2+2AB = A2+B2+2ABcos\Theta
cos\Theta = 1
So \Theta = 0.
Hope it clears. If you like answer then please approve it.

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