# A VECTOR OF MAGNITUDE ‘a’ IS ROTATED THROUGH ANGLE THETA.WHAT IS THE MAGNITUDE OF THE CHANGE IN THE VECTOR?

shashi K Sharma
46 Points
9 years ago
Dear Bharat
As the vector has been rotated by angle theta,
Let the final vector be called as vf , while the initial being vi
The magnitude of change in vector is | v – vi | = ( vi2 + vf2 - 2vivfCos(theta))^0.5
as the magnitude is same say ‘v’
thus the expression reduces to 2vSin(theta/2)

Kindly note that change in magniyude is zero while magnitude of change in vector is 2vSin(theta/2)
Hope this rustic expression is not that pesky.
Bharat Makkar
34 Points
9 years ago
THANKS FOR ALL THE ANSWERED PROBLEMS.
3 years ago
Dear student,

As the vector has been rotated by angle θ,
Let the final vector be called as vf , while the initial being vi
The magnitude of change in vector is | v – vi | = ( vi2 + vf2 - 2vivfCosθ)1/2
as the magnitude is same say , |vi| = |vf| = v
thus the expression reduces to 2vSin(θ/2)
Kindly note that change in magnitude is zero while magnitude of change in vector is 2vSin(θ/2)

Thanks and regards,
Kushagra