Answer:
α = 164.5387822595581°
Step-by-step explanation:
Calculate dot product:
a · b = ax · bx + ay · by = 5 · (-7) + (-4) · 3 = - 35 - 12 = -47
Calculate magnitude of a vector:
|a| = ax2 + ay2 = 52 + (-4)2 = 25 + 16 = 41
|b| = bx2 + by2 = (-7)2 + 32 = 49 + 9 = 58
Calculate angle between vectors:
cos α = a · b
|a|·|b|
cos α = -47
41 · 58
= - 47
2378
√2378 ≈ -0.9638111202541978
α = 164.5387822595581°
