Calculate, correct to one decimal place, the angle betwee...
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+32) = √(4 + 9)
|b| = √13
= 26 = 13√13 x cos θ
= 2613√13 = cos θ
=2√13 = cos θ
= θ = cos−1(2√13)
∴ θ = 56.3º