1. Sec 7.2 – Basic Vector Operations Name:

1. Create the following vector statement in the graph to determine the resultant vector in rectangular form.

A. Using the information below graphically determine 풑⃗ + ⃗+ ퟐ풎⃗

B. Algebraically find 2p j m

C. Using the information below graphically determine 풌⃗ − ퟑ풒⃗ + ퟐ풏⃗

D. Algebraically find 3 2k q n

Show work here

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2 :

p

j

m

1b.

1a.

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3 :

2 :

k

q

n

1d.

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1c.

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M. Winking © Unit 7-2 pg. 128

2. Let the following vectors be defined: 풗⃗: ⟨−ퟑ,ퟓ⟩ 풖⃗: ⟨ퟕ,ퟐ⟩ 풑⃗: ⟨ퟒ,−ퟗ⟩

A. Simplify the following vector expression 풗⃗ + ퟐ풖⃗ and write your answer in component form.

B. Simplify the following vector expression ‖풑⃗ − 풗⃗‖ (i.e. What is the magnitude of the resultant vector?)

C. Find the direction of the vector expression

풗⃗ + 풖⃗ + 풑⃗.

D. Simplify the following vector expression 2풖⃗ + 풑⃗ and write your answer in polar form.

3. Let the following vectors be defined: 풑⃗: ⟨ퟒ,ퟑퟎ°⟩ 풒⃗: ⟨ퟑ,ퟏퟐퟎ°⟩

A. Rewrite vector 풑⃗ in rectangular form.

B. Rewrite vector 풒⃗ in rectangular form.

C. Determine 풑⃗+ 풒⃗ in rectangular form.

D. Determine 풑⃗+ 풒⃗ in polar form.

2a. 2b.

2c. 2d.

3a.

3b.

3c.

3d.

M. Winking © Unit 7-2 pg. 129

4. Let the following vectors be defined: 풑⃗: ⟨ퟒ,ퟑퟎ°⟩ 풒⃗: ⟨ퟑ,ퟏퟐퟎ°⟩

Determine 풑⃗+ 풒⃗ in polar form.

(Use law of Cosines to determine your answer.)

5. Let the following vectors be defined: 풂⃗: ⟨ퟐ,ퟒퟎ°⟩ 풃⃗: ⟨ퟒ,ퟑퟒퟎ°⟩

A. Rewrite vector 풂⃗ in rectangular form.

B. Rewrite vector 풃⃗ in rectangular form.

C. Determine 풃⃗ − 풂⃗ in rectangular form.

D. Determine 풃⃗ − 풂⃗ in polar form.

E. Determine ퟓ풂⃗ in polar form.

6. Let the following vectors be defined: 풎⃗: ⟨ퟑ,ퟏퟑퟒ°⟩ 풏⃗: ⟨ퟔ,ퟑퟑ°⟩

Determine 풎⃗+ 풏⃗ in polar form.

(Use law of Cosines to determine your answer.)

5a.

5b.

5c.

5d.

M. Winking © Unit 7-2 pg. 130

4.

5e.

6.