The sum of two unit vectors is also a unit vector. The magnitude of the difference of these two vect

Question

The sum of two unit vectors is also a unit vector. The magnitude of the difference of these two vectors is

Professor PC Thomas Classes · Answer

(a) : Let the unit vectors be $\hat{a}$ and $\hat{b}$. Given $|\hat{a}+\hat{b}| = 1 \implies \sqrt{1^2+1^2+2(1)(1)\cos	heta} = 1 \implies 2+2\cos	heta = 1 \implies \cos	heta = -1/2$. \ The magnitude of their difference is $|\hat{a}-\hat{b}| = \sqrt{1^2+1^2-2(1)(1)\cos	heta} = \sqrt{2-2(-1/2)} = \sqrt{2+1} = \sqrt{3}$.