Question

Need Help with Dot Products of Vectors! please help!

Answer 1

what is equation for finding work done by a constant force F along a vector?

Answer 2

Given the directional angle as well.

Answer 3

So this is the situation:

Answer 4

To get from A to B, only part of the 180 pounds work in the right direction.
This part can be found by considering the force as the sum of two components, one in the direction of AB, the other perpendicular to AB:

Answer 5

In the last drawing, the red vector is the component that helps moving from A to B.
As you can see, it is less than 180 pounds.
Do you know how to calculate how big it is?

Answer 6

You could calculate it without using the dot product of vectors. It is just a 30-60-90 degrees triangle.

But as you refer to the dot product, you will be aware that the work done is equal to the dot product of the vectors AB and the vector that represents the force.

With the formula for the dot product:

dot product of u and v = (length of u) x (length of v) x cosine of angle between u and v

you should be able to get the right answer.
Tell me if you still have problems!