Straight LineMedium
Question
Let 0 < α < 
be a fixed angle. If P = (cos θ, sin θ) and Q = {cos(α - θ), sin (α - θ)}, then is obtained from P by
be a fixed angle. If P = (cos θ, sin θ) and Q = {cos(α - θ), sin (α - θ)}, then is obtained from P byOptions
A.clockwise rotation around origin through an angle α
B.anticlockwise rotation around origin through an angle α
C.reflection in the line through origin with slope tan α
D.reflection in the line through origin with slope tan
Solution
In the Argand plane P is represented by eiθ and Q is represented by ei(α - θ)
Now, rotation about a line with angle α is given by eiθ → ei(2α - θ). Therefore, Q is obtained from P by reflection in the line making an angle α/2
Now, rotation about a line with angle α is given by eiθ → ei(2α - θ). Therefore, Q is obtained from P by reflection in the line making an angle α/2
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