[align=left]Vector Questions

1. Consider three vectors:



a. Draw the three vectors.
b. What is the length or magnitude of , and ?
c. What is the angle between and , and , and ?

2. Consider three vectors:



a. What is the length or magnitude of , also written as ?
b. Write the expression for 2 .
c. What is ?
d. What is ?
e. What is ?
f. What is the magnitude of ?
g. What is ?
h. What is the angle between and ?
i. Does equal ?
j. How is and related?
k. Give an example of the use of dot product in Physics and explain.
l. Give an example of the use of cross product in Physics and explain.
m. Imagine that the vector is a force whose units are given in Newtons. Imagine vector is a radius vector through which the force acts in meters. What is the value of the torque , in this case?
n. Now imagine that continues to be a force vector and is a displacement vector whose units are meters. What is the work done in applying force through a displacement ?
o. What is the vector sum of a vector given by 40 m, 30 degrees and a vector given by 12 m, 225 degrees? Use the method of resolving vectors into their components and then adding the components.


3. Consider three vectors:



A. Find .
b. Find .
c. Find .[/align][align=center][/align][align=right][/align]