Problem 5: Vector F having magnitude 5.5 N makes 10° with x-axis and vector r with magnitude 4.3 m makes 80° with x-axis. What is the magnitude of their dot and scalar products?
Note: This is important to note that in the scalar or vector product, the angle θ is the angle between the two vectors. In the given problem, we are given angles the vectors make with the x-axis. The angle between them can be calculated by subtracting angle of one vector from the other. To understand the point, consider the diagram below.
Now the angle of F with x-axis is, θ1 = 10° and the angle of r with x-axis is θ2 = 80°. Therefore, angle between F and r is 80° – 10° = 70° = θ. The given magnitudes of F = 5.5 N and r = 4.3 m. So,
Similarly, the cross product is given as