Name: ___________________________
Date: _____________________
Pd: _____
Honors Pre Calculus Chapter 8 Vectors Test
(Alternate Version)
Exact Value Section: While a calculator MAY be used all work must be shown and all answer placed in
rationalized, reduced, exact value form (NO DECIMAL ANSWERS).
Take Home
1. Vocabulary: Answer the following briefly:
a.
b.
c.
d.
e.
What are the two components of a vector?
What vector operation verifies perpendicularity?
What vector operation identifies a vector perpendicular to the plane?
What is the magnitude of any unit vector?
What is the difference between a vector and a scalar?
2. A ship leaving port sails for 180 miles in a direction 60º south of due east. Find the magnitude of the
vertical and horizontal components (exact value answer).
3. Find the magnitude of AB for A(10,-5) and B(3,5).
4. Write CD as the sum of unit vectors for C(2,12,1) and D(-4,-5,4).
5. Identify the vector opposite 683, −25, −704 :
6.
−5, 2, −14 =
7. Given that: a = a1, a2 , a3 , Show that a × −a = 0
8. Given that a = 7, −2 , b = 8, −5
a.
b.
c.
d.
Find −3a − 4b
Represent a + b graphically
Find a • b
Are the vectors perpendicular? (Defend your answer mathematically)
9. Given that u = 2, −3, 4 , v = 7, −2, 6
a.
b.
c.
d.
Represent vector u graphically.
Find 5u − 4v
Find u iv and identify if the vectors are perpendicular.
Find u × v , and verify your answer is perpendicular to the vectors above.
10.Given the points (8, 6, 5), (-10, 1,-2), and (-8, 10, 3) are on a plane Z.
a. Identify a vector perpendicular to plane z.
b. Identify a UNIT VECTOR perpendicular to plane z.
(End Exact Value only section)
Name: ___________________________
Date: _____________________
Pd: _____
Decimals are allowed for final answers and should be rounded to the hundredth.
380N
200N
11.Find the magnitude and direction of the resultant vector for the diagram right:
12.If a force F1 of 30N pulls an object at an angle 25º above due west and a force F2 of 35N pulls the
object at an angle of 55º below due east, Find the magnitude and direction of the resultant force.
13.A ship travels on a still water at a speed of 48 mph in a direction 40º North of West, If the ship passes
into a current moving12mph in the direction of due south. What will the ships resultant speed and
direction become given the affect of this water current?
14.Given a line that passes through the point (5,-1) is parallel to the vector a = 3, −6 :
a. express the line as a vector equation
b. express the line using two parametric equations
15.A line is given by the following parametric equations: x = 3t + 7 and y = 6t − 5
a. Express the line in slope intercept form.
b. What is the point on the line where t=10?
16. Two ships locations are plotted on an x-y radar grid. If the path of ship one is shown by
x − 4, y − 1 = t 2,3 and that of ship two by the vector equation x − 16, y + 7 = t −1,5 :
a. At what point on the x-y grid will the ships paths cross?
b. Will the ships hit each other, if so in how much time assuming t is in minutes?
17.Gray hits a baseball off of a tee that is four feet high. The initial velocity of his hit is 100 feet per second
at an angle of 44º above the horizontal in a positive direction. Given this information:
a. What is the initial horizontal and vertical velocity of the ball?
b. Write parametric equations for the horizontal distance and vertical displacement covered by the
ball.
c. How much time is the ball in the air for?
d. What is the range of the ball?
e. What is the maximum height the ball reaches?
Bonus:
Identify the equation of a plane in standard form Ax + By + Cx + D = 0 that contains the three points given in
problem 10. Demonstrate that your answer holds true for all three points given.