if the magnitude of the sum of the vectors is equal to their differenc

1.	if the magnitude of the sum of the vectors is equal to their difference of their magnitude,then the angle between the vectors is
Answer» Logically, how can magnitude of vector sum be equal to difference of their magnitudes. Obviously if the vectors are in opposite directions. This means the angle has to be 180. Mathematically, Let the vectors beaandbwith 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+2abcosx Difference in their magnitudes is a-b Hence, √(a^2+ b^2+2ab cosx) = a-b Squaring both sides, a^2+b^2+2ab cos x = a^2+ b^2–2ab 2ab cosx+2ab =0 2ab(cosx +1) =0 Since 2ab can't be zero, Cos x+1=0 Cosx=-1 X=180

if the magnitude of the sum of the vectors is equal to their difference of their magnitude,then the angle between the vectors is

Answer»

Logically, how can magnitude of vector sum be equal to difference of their magnitudes. Obviously if the vectors are in opposite directions. This means the angle has to be 180.

Mathematically,

Let the vectors beaandbwith 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+2abcosx

Difference in their magnitudes is

a-b

Hence,

√(a^2+ b^2+2ab cosx) = a-b

Squaring both sides,

a^2+b^2+2ab cos x = a^2+ b^2–2ab

2ab cosx+2ab =0

2ab(cosx +1) =0

Since 2ab can't be zero,

Cos x+1=0

Cosx=-1

X=180

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