Answer to Question #247464 in Physics for Jen

Question

Dot or Scalar Product

1. Calculate the dot product of vectors a and b where a is 4 units and b is 8 units and angle Theta is 67

Answer 1

By definition, the dot product is:

$$(\mathbf{a},\mathbf{b}) = ab\cos\theta$$

where $a = 4, b = 8$ are the magnitudes of the vectors, and $\theta = 67\degree$ is the angle between them. Thus, obtain:

$$(\mathbf{a},\mathbf{b}) = 4\cdot 8\cdot \cos67\degree \approx 12.5$$

Answer. 12.5.