Question

A vector of magnitude a is rotated through an angle theta What is magnitude of the change in the vector???

Answer 1

For rotation, the magnitude remains unchanged.

Answer 2

but the answer given in my book is " \[2a \sin \theta / 2\] '

Answer 3

It asks for the magnitude of the vector which is the (change in vector). This sounds a bit confusing. Consider a particle at a position \(\vec r_1\) from the origin. Now it rotates by an angle \(\theta\) and the corresponding new position is \(\vec r_2\). What is the change in vector ? (= \(\vec r_2 - \vec r_1 = \Delta \vec r\))

The question asks the magnitude of \(\Delta \vec r\).

To get the magnitude, draw the figure, it should be an isosceles triangle. Drop the altitude from the top to the bottom side (unequal side) and then use basic trig to get the magnitude.