Question

Find if α = 2, β = 2, and the angle between α and β is π/4 radians.

A) α • β = 0
B) α • β = 4
C) α • β = 2√2
D) α • β = 2

Answer 1

To find the dot product of the vectors α = 2 and β = 2, we use the formula for dot product: α • β = |α||β|cos(θ), where |α| and |β| represent the magnitudes of the vectors and θ is the angle between them.
In this case, |α| = 2 and |β| = 2. Since the angle between α and β is π/4 radians, we can substitute these values into the formula:
α • β = 2 * 2 * cos(π/4) = 4 * √2/2 = 2√2.
Therefore, the correct answer is C) α • β = 2√2.

Step-by-step explanation:

To find the dot product of the vectors α = 2 and β = 2, we use the formula for dot product: α • β = |α||β|cos(θ), where |α| and |β| represent the magnitudes of the vectors and θ is the angle between them.

In this case, |α| = 2 and |β| = 2. Since the angle between α and β is π/4 radians, we can substitute these values into the formula:

α • β = 2 * 2 * cos(π/4) = 4 * √2/2 = 2√2.

Therefore, the correct answer is C) α • β = 2√2.