Question

A vector a is rotated an angle 2π,the magnitude of new vector is A explain
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Answer 1

Answer: By rotating a vector it's magnitude does not change.

Here, angle between original vector A and vector obtained after rotation, A' is (theta).

Using law of triangle we have,

A+ dA=A', where |A|=|A'|.

Therefore,

(A'-A)^2 =(dA)^2 or

A^2+ A^2 -2A^2 cos(theta)=(dA)^2

2A^2[1-cos (theta)]=(dA)^2

2A^2[2 sin^2(theta/2)]= (dA)2

Therefore ,dA=2A sin(theta/2). This is magnitude of change in vector

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