Under what condition the magnitude of the sum of two vector is equal to the magnitude of difference between them
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Let A bar and B bar be two vectors.
We have,
A bar + B bar = A bar - B bar
Applying modulus on both sides we have,
lA bar + B barl = lA bar - B barl
√(A²+B²+2ABcosà) = √(A²+B²-2ABcosà)
Here à is the angle between the two vectors.
2ABcosà=-2ABcosà
4ABcosà=0
cosà=0
à=90
Hence if two vectors are perpendicular to each other then the magnitude of the sum of the two vectors is equal to the magnitude of the difference between them.
We have,
A bar + B bar = A bar - B bar
Applying modulus on both sides we have,
lA bar + B barl = lA bar - B barl
√(A²+B²+2ABcosà) = √(A²+B²-2ABcosà)
Here à is the angle between the two vectors.
2ABcosà=-2ABcosà
4ABcosà=0
cosà=0
à=90
Hence if two vectors are perpendicular to each other then the magnitude of the sum of the two vectors is equal to the magnitude of the difference between them.
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