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Cogito

AP Precalculus · Chapter 8 · Lesson 2

Practice Worksheet

Vectors

Quantities with direction attached.

12 problems · about 21 minutes · AP Precalculus 4.4, 4.5

NameDate

Figure — use these to answer the problems

The dashed arrow shows the second vector starting where the first ends. Its tip is the resultant.
  • Vector a(3, 0) · length 3
  • Vector b(0, 4) · length 4
  • a + b(3, 4) · length 5
First vector, x component3
First vector, y component0
Second vector, x component0
Second vector, y component4
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. What is the magnitude of (9, 12)?

    Answer

  2. Why can magnitudes not simply be added?

    • Direction matters, so components add rather than lengths.
    • Because of rounding.

  3. Magnitude of (6, 8)?

    Answer

  4. Magnitude of (5, 12)?

    Answer

  5. (1, 5) + (4, 2). What is the y component?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. 4 times the vector (3, 2). What is the y component?

    Answer

  2. Magnitude of (0, 9)?

    Answer

  3. Is mass a vector? 1 yes, 0 no.

    Answer

Stretch Yourself

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

4 problems

  1. Sort each quantity by whether it is a vector.

    Write each item under the heading it belongs to: Velocity · Force · Mass · Temperature

    Vector

    Not a vector

  2. Magnitude of (8, 6)?

    Answer

  3. The Magnitude

    What is the magnitude of the vector (3, 4)?

    Answer

  4. The Sum

    (2, 3) + (5, 1). What is the x component of the sum?

    Answer