Ace Trigonometry
Vector/Parametric Review
Read the directions carefully.
Use the following vectors for problems 1-3 .
Magnitude = 1.8 cm
Direction = 144۫
a
1.) Find the components of
b
Magnitude = 2.7 cm
Direction = 225۫
a and b
a =____________________
b =__________________
Sketch the resultant vector. Round your magnitude to the nearest tenth of a centimeter. Find the
components of the resultant. Find the magnitude and direction of the resultant.
2.) a  b
3.) 2a  b
1.) Magnitude: _________
2.) Magnitude: _________
Direction: __________
Direction: __________
4.)
5.)
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
6.)
u  2v  w
7.)
u  s  2r
8.) u 
1
rs
3
9.) 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: _________
10.) 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: _________
11.) Write EF
Magnitude: _________
as the sum of unit vectors for E (5,1, 4) and F (9,3,1) .
Find each dot product and state whether the vectors are orthogonal. Find angle between vectors.
12.) 2,0  0, 5
13.) 3, 4, 2  2, 2,1
Dot Product: _____________
Dot Product: _____________
Orthogonal?: ____________
Orthogonal?: ____________
Angle: ________________
Angle:________________
Find each cross product and state the vector orthogonal to each vector in ai +bj + ck form.
14.) 2, 1,3  1,0, 5
15.) 2,2, 1  0, 2,2
16.) Verify that the vector found in #14 is orthogonal to each original vector (Show dot product is 0).
17.) Find the magnitude and direction of the resultant vector from the diagram below.
18.) 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: _________
19.) 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.
20.) y  2 x  4
21.)
3x  2 y  4
Write an equation in slope-intercept form of the line with the given parametric equations.
1
7
22.) x   t  6; y  2t  4
23.) x  2t  5; y  4t 
2
4
24.)
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?
25.) A ball is thrown with an initial velocity of 56 feet per second at an angle of 30° with the ground.
a.) If the ball is thrown from 8 feet about ground, 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?