Final answer:
The dot product of vectors a and b is calculated using the formula a · b = |a| · |b| · cos(2/3). With the given magnitudes, the calculation involves multiplying 4, 3, and the cosine of 2/3 radians.
Step-by-step explanation:
To find the dot product of vectors a and b, we can use the formula from the provided information that relates the dot product to the magnitudes of the vectors and the cosine of the angle between them.
The formula for the dot product given the magnitudes of two vectors |a| and |b|, and the cosine of the angle φ between them is:
a · b = |a| · |b| · cos(φ)
The values provided are |a| = 4, |b| = 3, and the angle between a and b is 2/3 radians. Utilizing these values in the formula, we get:
a · b = 4 · 3 · cos(2/3)
To solve for the actual numerical value, you can use a calculator to find the cosine of 2/3 radians and then multiply it by 4 and 3. This will yield the final value for the dot product of vectors a and b.