Write each of v and w in polar form:
v = √(32 + 42)[cosθ + i sinθ], where θ = tan-1(4/3) = 53.1°
= 5[cos53.1° + i sin53.1°]
w = √(42 + 32)[cosλ + i sinλ], where λ = tan-1(3/4) = 36.9°
= 5[cos36.9° + i sin36.9°]
Angle between v and w is 53.13° - 36.87° = 16.26°
NOTE: If you know what dot product is and how to find the norm (magnitude) of a vector, then another way to find the angle, β, between v and w is to use the formula:
cosβ = v · w = (3)(4) + (4)(3) = 24
llvll llwll (5)(5) 25
So, β = cos-1(24/25) = 16.26°
