Question

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

Answer 1

Answer:

Angle between the two vectors is 20.7718°.

Step-by-step 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║= $\sqrt{1+4+9+16}$ = $\sqrt{30}$

║y║= $\SQRT{16+4+16+25} = \sqrt{61}$ '

Thus, we get

40 = $\sqrt{30}$×$\sqrt{61}$×Cos θ

Thus, Cos θ = $\frac{40}{\sqrt{30}\sqrt{61}}$

Cos θ = 0.935

θ = $Cos^{-1} (0.935)$

θ = 20.7718°