Consider the vectors x=(1,2,3,4) and y=(4,2,4,5) in r4 . find the angle between them.

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║= =

║y║= '

Thus, we get

40 = ××Cos θ

Thus, Cos θ =

Cos θ = 0.935

θ =

θ = 20.7718°

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is symmetric about the line y = 120,000.

step-by-step explanation: