The Dot Product

A number that measures agreement.

12 problems · about 23 minutes · N-VM.B.4, N-VM.C.11

NameDate

Figure — use these to answer the problems

Make the two vectors perpendicular and check that the products of the components cancel.

u, x-component4

u, y-component2

v, x-component-2

v, y-component4

Figure 1

Straightforward practice. Get the method working first.

5 problems

⟨2, −1, 3⟩ · ⟨1, 4, 1⟩. What is the result?
Answer
2
A dot product of zero tells you what?
- The vectors are perpendicular.
- The vectors are equal.
⟨1, 2, 3⟩ · ⟨4, 5, 6⟩. What is the result?
Answer
⟨1, 0, 0⟩ · ⟨0, 1, 0⟩. What is the result?
Answer
u · u where u = ⟨3, 4, 0⟩. What is the result?
Answer

The same ideas with more to keep track of.

3 problems

Two vectors of length 5 and 4 meet at 60 degrees. What is the dot product?
Answer
A dot product is negative. Is the angle greater than 90 degrees? 1 yes, 0 no.
Answer
⟨5, 0, 0⟩ · ⟨−3, 8, 9⟩. What is the result?
Answer

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

4 problems

9
Match each dot product value to what it says about the angle.
Draw a line from each item on the left to its match on the right.
- Positive
- Zero
- Negative
- Less than 90 degrees
- Exactly 90 degrees
- More than 90 degrees
u and v both have length 2 and point the same way. What is u · v?
Answer
The Sled
A force ⟨6, 0, 0⟩ newtons moves a sled ⟨4, 3, 0⟩ metres. How much work is done, in joules?
Answer
The Right Angle
⟨2, k, 0⟩ is perpendicular to ⟨6, 3, 0⟩. What is k?
Answer