The magnitude of the sum of two vectors and the difference of the
two vectors are equal. Then the
two vectors are inclined to each other at an angle of
Answers
Answered by
16
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
Hopefully it will help youand sorry if it is wrong
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
Hopefully it will help youand sorry if it is wrong
Answered by
8
Answer:
its answer is x - 180.........
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