Question

A vector A of magnitude A is turned through an angle Alfa. calculate the change in the magnitude of vector​

Answer 1

Explanation:

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

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(alfa)=(dA)^2

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

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

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

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Answer 2

Explanation:

here, angle between original vector A and vector obtained after rotation , A' is (alfa)

therefore ,

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

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

2A ^ 2( 1 - cos (alfa) = (dA) ^ 2

2A^ 2( 2 sin^ 2 (alfa / 2) = (dA) 2

therefore , dA = 2A sin (alfa /2)