Vectors and Their Arithmetic

Arrows you can add and stretch.

12 problems · about 22 minutes · N-VM.A.1, N-VM.B.4, N-VM.B.5

NameDate

Figure — use these to answer the problems

Move both vectors and watch the sum. The resultant is drawn from the start of the first arrow to the tip of the second.

u, first entry3

u, second entry1

v, first entry1

v, second entry4

Figure 1

Straightforward practice. Get the method working first.

5 problems

3⟨2, 4⟩ + ⟨1, 0⟩. What is the first entry?
Answer
2
What does multiplying a vector by −2 do geometrically?
- Doubles the length and reverses the direction.
- Turns it 90 degrees.
⟨2, 7⟩ + ⟨5, 1⟩. What is the first entry?
Answer
⟨2, 7⟩ + ⟨5, 1⟩. What is the second entry?
Answer
4⟨3, −2⟩. What is the second entry?
Answer

The same ideas with more to keep track of.

3 problems

Mixed problems. Work out what kind of question it is before you start.

4 problems

9
Match each operation to its geometric effect.
Draw a line from each item on the left to its match on the right.
- Adding two vectors
- Multiplying by 3
- Multiplying by −1
- Placing the second arrow at the tip of the first
- Stretching to three times the length
- Turning the arrow to point the opposite way
⟨5, 9⟩ + ⟨0, 0⟩. What is the first entry?
Answer
The Two Legs
A walk of ⟨4, 2⟩ then ⟨3, 5⟩ blocks. What is the first entry of the total displacement?
Answer
The Triple
3 times the vector ⟨2, −5⟩. What is the second entry?
Answer