Precalculus Honors B
Vectors Unit Review
Name ____________________________
Read the directions carefully.
1.)
2.)
The vector v has a magnitude of 5 meters and a direction of 60°. Find the magnitude of its horizontal and
vertical components.
2
The vector u has a magnitude of 10 cm. If v   u , what is the magnitude of v to the nearest tenth?
5
u in each equation if
v  2, 3 , w  1,5 , r  1, 1,1 , and s  0, 3, 2 .
Find an ordered pair or ordered triple to represent
3.)
u  2v  w
4.)
u  s  2r
5.)
6.) Write the ordered pair that represents the vector from A(3, 1) to B(1, 2) .
Then find the magnitude of AB .
Ordered Pair: _________
Magnitude: _________
7.) Write the ordered triple that represents the vector from X (1,3,5) to Y (3,0,1) .
Then find the magnitude of XY .
Ordered Triple: _________
8.) Write EF
Magnitude: _________
as the sum of unit vectors for E(5,1, 4) and F (9,3,1) .
1
u  r s
3
Find each inner product and state whether the vectors are perpendicular. Write yes or no.
9.) 2,0  0, 5
10.) 3, 4, 2  2, 2,1
Inner Product: _____________
Inner Product: _____________
Perpendicular?: ____________
Perpendicular?: ____________
Find each cross product. (Be prepared to verify your solution as well.)
11.) 2, 1,3  1,0, 5
12.) 2, 2, 1  0, 2, 2
13.) Find the magnitude and direction of the resultant vector from the diagram below.
14.) A 10-newton force acting at 45° and a 20-newton force acting at 130° act concurrently on an object. Find
the magnitude and direction of the resultant force.
Magnitude: _________
Direction: _________
15.) Write a vector equation of the line that passes through point P(3, 2) and is parallel to a  2, 6 .
Then write parametric equations of the line. Lastly, graph the line.
Graph:
Vector Equation: ________________
Parametric Equations:
__________________
__________________
Write parametric equations for each equation.
16.) y  2 x  4
17.)
3x  2 y  4
Write an equation in slope-intercept form of the line with the given parametric equations.
1
7
18.) x   t  6; y  2t  4
19.) x  2t  5; y  4t 
2
4
20.)
Shannon kicks a soccer ball with an initial velocity of 45 feet per second at an angle of 12° with the
horizontal. After 0.5 seconds, what is the height of the ball?
21.) A ball is thrown from 8 feet above the ground with an initial velocity of 56 feet per second at an angle of
30° with the ground.
a.) When will it hit the ground?
b.) How far will the ball travel horizontally before hitting the ground?
c.) What is the maximum height of the ball?