Vectors Work Sheet Name: _________________
1. Which of these vectors is the same (or equivalent)?
For one vector to be equivalent (or equal to another) what has to be true?___________________________________________________________________________________________________________
Name the end points for these vectors and write these vectors as ordered pairs
For each of the vectors above, write them also using unit vector notation (using notation).
A vector B = (7, 1, 9) the xcomponent is _________ the ycomponent is __________, and the zcomponent is ________
What is the magnitude of the vector v = (1, 3)?
What angle does the vector v = (1, 3) make with the positive xaxis?
In the diagram below, are the vectors A and B being added correctly?
Draw the addition (and the resultant vector) as it should have been:
Does the resultant vector look the same? (It shouldn’t!)
8. Add these vectors, given their components:
Vector 1 
Vector 2 
Sum 
(1, 1) 
(3, 4) 

(1, 2, 4) 
(5, 0, 2) 

(0, 1, 0) 
(1, 0, 0) 

(2.4, 0.9) 
(1, 0.3) 

Determine the x and y components of these vectors:
(Draw a sketch of each)
magnitude 9, angle 30^{o }with the positive xaxis.
Magnitude 11, angle 60^{o} with positive xaxis
Magnitude 60 m/s at an angle of 45^{o} above the xaxis
Magnitude 17 N/C at an angel of 115^{o} with the positive xaxis
Write each of your vectors in question 9 above in unit vector notation.
a)
b)
c)
d)
a) If the vector u = (3, 4) has magnitude 5, what is the magnitude of the vector 2u?
What angle do each of these make with the positive xaxis?
Does multiplying a vector by a positive number change its direction?
Does multiplying a vector by a negative number change its direction?
If the vector u = (3, 4), what is  u?
Write both in unit vector notation.
Do the vector subtraction:
Vector 1 
Vector 2 
Difference (vector 1 – vector 2) 
(1, 1) 
(3, 4) 

(1, 2, 4) 
(5, 0, 2) 

(0, 1, 0) 
(1, 0, 0) 

(2.4, 0.9) 
(1, 0.3) 
