Question

Find a ·
b. |a| = 8, |b| = 7, the angle between a and b is 2π/3

Answer 1

The dot product of vectors a and b with magnitudes 8 and 7 respectively and an angle of 2π/3 between them is found using the formula a · b = |a| × |b| × cos(θ), resulting in a dot product of -28.

Step-by-step explanation:

The student is asking to find the dot product of vectors a and b given their magnitudes and the angle between them. In vector mathematics, the dot product is defined as a · b = |a| × |b| × cos(θ), where |a| and |b| are the magnitudes of vectors a and b respectively, and θ is the angle between the two vectors.

Given that |a| = 8, |b| = 7, and the angle θ is 2π/3, we can substitute these values into the dot product formula:

a · b = 8 × 7 × cos(2π/3)

Using a calculator, we find the cosine of 2π/3 and then multiply it by the magnitudes:

cos(2π/3) = -0.5 (as cos(120°) = -0.5)

a · b = 8 × 7 × (-0.5) = -28

Answer 2

By definition we have that the scalar product of two vectors is given by:
a.b = | a |. | b | .cos (angle)
Substituting the values
a.b = (8) * (7) * (cos (2π / 3)) = - 28