Calculate, correct to one decimal place, the angle between 5 i + 12 j and -2 i + 3 j
56.3º
76.3º
66.4º
54.8º
Correct answer is A
Using the dot product:
a.b = |a||b|cos θ
a.b = 5(-2) + 12(3) = -10 + 36 = 26
|a| = √(52 + 122) = √(25 + 144)
|a| = √169 = 13
|b| = \(√((-2)^2 + 3^2)\) = √(4 + 9)
|b| = √13
= 26 = 13√13 x cos θ
= \(\frac{26}{13\sqrt13}\) = cos θ
=\(\frac{2}{\sqrt13}\) = cos θ
= θ = \(cos^{-1} (\frac{2}{\sqrt13})\)
∴ θ = 56.3º