Question

Assuming the x-axis is horizontal to the right for the vectors in the following figure, find the following scalar products:

Answer 1

To find the scalar products of the vectors, resolve each vector into its horizontal and vertical components and use the formula A · B = A * B * cos(theta).

Step-by-step explanation:

To find the scalar products of the vectors, we need to resolve each vector into its horizontal and vertical components. The horizontal component is given by Ax = A * cos(theta), and the vertical component is given by Ay = A * sin(theta), where A is the magnitude of the vector and theta is the angle it makes with the positive x-axis.

1. (a) To find the scalar product A · C, we multiply the magnitudes of the vectors and the cosines of the angles between them: A · C = A * C * cos(theta).
2. (b) To find the scalar product A · F, we use the same formula: A · F = A * F * cos(theta).
3. (c) To find the scalar product D · C, we again use the formula: D · C = D * C * cos(theta).