Math 4
Name:
Date:
Quiz Review
Sections 3.4 – 3.6
Key Facts
• To add vectors, place the “tail” of one vector (the side without the arrow) at the
“tip” of the other vector (the side with the arrow). Draw the vector sum from the
tail of the first vector to the tip of the second vector.
• To subtract vectors, rewrite the difference 𝑥 − 𝑦 as 𝑥 + (−𝑦). Remember −𝑦 is
the same as 𝑦 except that it points in the opposite direction (the arrow is on the
other end). Add 𝑥 and −𝑦 using the tip to tail addition method.
• To multiply a vector a by a constant (a number), means to scale the vector,
making it bigger or smaller.
o Multiplying by a positive constant does not change the direction of the
vector
o Multiplying by a negative constant will reverse the direction of the vector
(arrow is on the other end)
• A vector has a horizontal and a vertical component. Use right triangle
trigonometry (SOH CAH TOA) to calculate the components.
o We can find the components of a sum or difference vector by adding or
subtracting the components of the original two vectors.
o When we multiply a vector by a constant, the resulting vector’s
components are also multiplied by the constant.
Make sure your homework is up-to-date: #1-27 in your workbook should be done.
Practice
1. Use the vectors below to draw the following. Label all the vectors you draw.
Your resulting vector should be in a different color.
r r
a. x + z
ur r
b. w + y
ur
c. 2w
r r
d. y − z
r r
e. 2y + x
r
f. −3x
r r
g. −y + x
ur r
h. 2w + z
i.
ur r
w + 2y
r r
j. y − 3x
3. Will walked 2 miles east, 4 miles south, 3 miles east and then 1 mile north. Draw a
vector to represent his total change in position.
4. A ship can travel 5 miles east in a day. The wind blows 3 miles north over the course
of that day. Draw a vector to represent the ship’s total change in position.
5. Find the horizontal and vertical components of the following vectors:
a.
b.
Horizontal:
Horizontal:
Vertical:
Vertical:
c.
Horizontal:
Horizontal:
Vertical:
Vertical:
6. a. Find the horizontal and vertical components of the following vectors:
𝑎
𝑐
𝑏
22 ft
32°
8 ft
45°
b. Find the horizontal and vertical components of 𝑏 + 𝑐
Horizontal:
Vertical:
c. Find the horizontal and vertical components of 𝑎 − 𝑐
Horizontal:
Vertical:
d. Find the horizontal and vertical components of 4 ∙ 𝑏
Horizontal:
Vertical:
20°
12 ft
7. a. A disabled ship is drifting at sea. First, the wind blows the ship 4 miles at angle 30°
south of true east. Then the ship hits a current which carries it 7.5 miles at an angle 50°
north of true east. How far has the ship traveled horizontally? Vertically?
b. What is the length and direction for the vector that represents the ship’s total change in
position?
Answers
5a. Horizontal: 8.62 Vertical: 11.03
b. Horizontal: -10.72 Vertical: 9
c. Horizontal: -35.57 Vertical: -10.20
d. Horizontal: -30.08 Vertical: 7.5
6a.
Horizontal
Vertical
𝑎
18.66 ft
11.66 ft
b. Horizontal: 5.62 ft
Vertical: 1.56 ft
𝑏
-5.66 ft
5.66 ft
𝑐
11.28 ft
-4.1 ft
c. Horizontal: 7.38 ft Vertical: 15.76 ft
d. Horizontal: -22.64 ft Vertical: 22.64 ft
7. a. Horizontal: 8.28 mi Vertical: 3.75 mi
b. Length: 9.09 mi, 𝜃 = 24.37°