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║= [tex]\sqrt{1+4+9+16}[/tex] = [tex]\sqrt{30}[/tex]
║y║= [tex]\SQRT{16+4+16+25} = \sqrt{61}[/tex] '
Thus, we get
40 = [tex]\sqrt{30}[/tex]×[tex]\sqrt{61}[/tex]×Cos θ
Thus, Cos θ = [tex]\frac{40}{\sqrt{30}\sqrt{61}}[/tex]
Cos θ = 0.935
θ = [tex]Cos^{-1} (0.935)[/tex]
θ = 20.7718°
