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Cogito

Precalculus · Chapter 3 · Lesson 2

Practice Worksheet

The Dot Product

Multiply two vectors and get a number.

12 problems · about 22 minutes · TEKS P.4.H, TEKS P.4.I

NameDate

Figure — use these to answer the problems

Set one vector to (3, 0) and the other to (0, 4). The dot product is zero, and they meet at a right angle.
  • Vector a(3, 1)
  • Vector b(-1, 3)
a, x component3
a, y component1
b, x component-1
b, y component3
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. (3, 2) · (1, 4)?

    Answer

  2. What does a dot product of zero mean?

    • The vectors are perpendicular.
    • The vectors are equal.

  3. (1, 2) · (3, 4)?

    Answer

  4. (5, 0) · (0, 7)?

    Answer

  5. (2, 3) · (2, 3)?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. (−2, 1) · (4, 2)?

    Answer

  2. Magnitude of (3, 4)?

    Answer

  3. a · b = 0. What is the angle between them, in degrees?

    Answer

Stretch Yourself

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

4 problems

  1. Sort each pair by what the sign of its dot product tells you.

    Write each item under the heading it belongs to: Dot product = 12 · Dot product = −5 · Dot product = 0.5 · Dot product = −20

    Angle under 90°

    Angle over 90°

  2. (4, 0) · (0, 9)?

    Answer

  3. The Product

    (2, 5) · (4, 1). What is the result?

    Answer

  4. The Right Angle

    (6, 2) · (−1, 3). What is the result?

    Answer