Scalar dot product

Calculate u.v if |u| = 5, |v| = 2 and when the angle between the vectors u, v is:

a) 60°
b) 45°
c) 120°

Correct answer:

a =  5
b =  7.0711
c =  -5

Step-by-step explanation:

u=5 v=2 α=60 ∘  a=u⋅ v⋅ cosα=u⋅ v⋅ cos60° =5⋅ 2⋅ cos60° =5⋅ 2⋅ 0.5=5
β=45 ∘  b=u⋅ v⋅ cosβ=u⋅ v⋅ cos45° =5⋅ 2⋅ cos45° =5⋅ 2⋅ 0.707107=7.071=7.0711
γ=120 ∘  c=u⋅ v⋅ cosγ=u⋅ v⋅ cos120° =5⋅ 2⋅ cos120° =5⋅ 2⋅ (−0.5)=−5

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