Find the angle between vectors A(1,3,4,1) and B(4,6,7,2)?

Answer 1

Use the dot product.

A • B = | A | | B | cosθ

A • B = <1, 3, 4, 1> • <4, 6, 7, 2> = 4 + 18 + 28 + 2 = 52

| A | = √(1² + 3² + 4² + 1²) = √27 = 3√3

| B | = √(4² + 6² + 7² + 2²) = √105

Take the dot product formula.

A • B = | A | | B | cosθ

cosθ = (A • B) / (| A | | B |) = 52 / [(3√3)(√105)]
cosθ = 52/(9√35)

θ = arccos[52/(9√35)] ≈ 12.413223°