First slide

Motion in a plane

Question

If the sum of two unit vectors is also a vector of unit magnitude, the magnitude of the difference of the two unit vectors is

Moderate

Solution

The sum of equal vectors of magnitude
R = 2P cosθ/2
In unit vectors ⇒1 = 2 x 1 x cosθ/2
$\large \cos \frac{\theta }{2} = \frac{1}{2} = \cos {60^0};\frac{\theta }{2} = {60^0} \Rightarrow \theta = {120^0}$
The magnitude of difference of equal vectors
$\large S = 2P\sin \frac{\theta }{2}$
In unit vectors
$\large \Rightarrow S = 2 \times 1 \times \sin \frac{{{{120}^0}}}{2} = 2 \times \frac{{\sqrt 3 }}{2} = \sqrt 3 units$

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