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Multiplication with Vectors

The rectangul...

Question

The rectangular components of a vector are $(2, 2)$ . The corresponding rectangular components of another vector are $(1, \sqrt{3})$ . Find the angle between the two vectors (in degree).

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Solution

Let
$\to A = 2^i + 2^j, \to B =^i + \sqrt{3}^j$
$θ$ be the angle between $\to A$ & $\to B$
$cos θ = \frac{\to A . \to B}{| A | | B |} = \frac{2 + 2 \sqrt{3}}{\sqrt{8} .2}$
$cos θ = \frac{\sqrt{3} + 1}{2 \sqrt{2}}$
$θ = 15^{\circ}$

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