Question

plz plz plz friends its urgent...
plz help me...
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show that if two vectors are equal in magnitude, their vector sum and difference are at right angles. ​

Answer 1

Answer:

Hey, it's a simple one.

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 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+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.

Hope it helps you .