Question

The rectangular component of a vector are (2,2) the corresponding rectangular components of a another vector are (1,root 3) find the angle between the two vectors

Answer 1

Let $\vec{a} = (2,2)$ and $\vec{b} = (1,\sqrt{3})$
We need the angle between the two vectors. Let angle be \theta , Then

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

Answer 2

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