Question

Consider the vectors x=(1,2,3,4) and y=(4,2,4,5) in R4 . Find the angle between them.

Answer 1

Angle between the two vectors is 20.7718°.

Explanation:

The given two vectors are x = (1,2,3,4) and y = (4,2,4,5)

Now the dot product between two vector is defined as

x.y = ║x║║y║cosθ

Now, x.y( dot product of x and y) = 1×4 + 2×2 + 3×4 + 4×5 = 40

║x║=
`√(1+4+9+16)` =
`√(30)`

║y║=
`\SQRT{16+4+16+25} = √(61)` '

Thus, we get

40 =
`√(30)`×
`√(61)`×Cos θ

Thus, Cos θ =
`(40)/(√(30)√(61))`

Cos θ = 0.935

θ =
`Cos^(-1) (0.935)`

θ = 20.7718°