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

Explanation

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