Question

The rectangular components of two vectors are (4.8,6.4) and (-17.32,10) , then the angle between the two vectors is?

Answer 1

Explanation:

Let \vec{a} = (2,2) and \vec{b} = (1,\sqrt{3})

We need the angle between the two vectors. Let angle be \theta , Then

\vec{a}.\vec{b}=ab\cos \theta \\ \\ So 2+2\sqrt{3}=(2\sqrt{2})(2)\cos\theta \\ \\ So \, \cos \theta = \frac {1+\sqrt{3}}{2\sqrt{2}} \\ So \, \theta = cos^{-1} \left( \frac {1+\sqrt{3}}{2\sqrt{2}} \right)