1.Given = (-2, 4, -1) and = (3, 2, -5), determine the following.

a)

b)

c) Scalar projection of on

d) Angle between and

2. A lawnmower is pushed 0.3 km by a force of 75N applied at an angle of 80 degree to the horizontal.

What is the amount of work done?

3. A mechanic applies 60N of force at the end of a 30cm wrench at an angle of 45 relative to the wrench.

What is the magnitude of the torque he is applying to the bolt being tightened? Draw a diagram.

4. A rusted bolt requires 25 Nm of torque to be loosened. If 60 N of force is applied, at an 85-degree angle, then how far from the center of rotation must the force be applied in order to loosen the bolt?

5. An object of mass 20kg is suspended by two pieces of rope that make an angle of 35 degree (left) and 40 degree (right) with a horizontal metal bar. Determine the tension in each of the two pieces of rope. Draw the equilibrium triangle, label the sides, and include all angles.

6. Given that the vectors =(6, -2, 2s) and =(-1, s + 1, 2) are perpendicular, what is the value of s?

7. How you would determine the components of a vector that is perpendicular to two vectors.

8. If the vector projection of on is a negative number, what can you conclude about the two vectors?

9. State whether each of the following will result in a vector, a scalar, or is meaningless...

a. + ________________

b. ( + ) ________________

c. ( + ) ________________