If a vector of length m is rotated through an angle beta about its tail.the change in its position of its head
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vector P = m cosФ i + m sinФ j
vector head P (m cosФ, m sinФ). vector tail = O(0,0)
After rotation, the angle becomes Ф+β.
So: new vector P' : m cos (Ф+β) i + m sin (Ф+β) j
change in the position: PP':
(PP')² = m² [ (cos(Ф+β) - cosФ)² + (sin(Ф+β) - sinФ)² ]
= m² [ (-2 sin β/2 sin(Ф + β/2) )² + (2 sin β/2 Cos(Ф+β/2) )² ]
= 4 m² sin² β/2 * 1
vector head P (m cosФ, m sinФ). vector tail = O(0,0)
After rotation, the angle becomes Ф+β.
So: new vector P' : m cos (Ф+β) i + m sin (Ф+β) j
change in the position: PP':
(PP')² = m² [ (cos(Ф+β) - cosФ)² + (sin(Ф+β) - sinФ)² ]
= m² [ (-2 sin β/2 sin(Ф + β/2) )² + (2 sin β/2 Cos(Ф+β/2) )² ]
= 4 m² sin² β/2 * 1
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