Calculate, correct to one decimal place, the angle between 5i + 12j and -2i +

Explanation

\(a . b = |a||b|\cos \theta\)

\((5i + 12j).(2i + 3j) = -10 + 36 = 26\)

\(26 = |5i + 12j||-2i + 3j|\cos \theta\)

\(|5i + 12j| = \sqrt{5^{2} + 12^{2}} = \sqrt{25 + 144} = 13\)

\(|2i + 3j| = \sqrt{2^{2} + 3^{2}} = \sqrt{4 + 9} = \sqrt{13}\)

\(26 = 13(\sqrt{13})\cos \theta\)

\(\cos \theta = \frac{26}{13\sqrt{13}} = 0.5547\)

\(\theta = 56.3°\)