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Learning Introductory Physics with Activities

Paul J. Emigh, Rebecka Tumblin, Kathryn Hadley, Danielle Skinner

Section 1.12 Magnitude and Direction

As you have seen, one of the most common shorthand ways of describing a vector is as something with “magnitude and direction”. Determining or working with these two quantities are essential for using vectors in physics.

Exercises Activities

1. Warm-up 1: Three Vectors.

Which of the following is \(\vec{C}\text{?}\)
Figure 1.12.1. Three vectors in a triangle.
  1. \(\displaystyle \vec{C} = \vec{A} + \vec{B}\)
  2. \(\displaystyle \vec{C} = \vec{B} + \vec{A}\)
  3. \(\displaystyle \vec{C} = \vec{A} - \vec{B}\)
  4. \(\displaystyle \vec{C} = \vec{B} - \vec{A}\)
  5. None of the above

2. Warm-up 2: Vector Component.

Find the \(y\)-component of the vector shown below.
Figure 1.12.2. A vector.

3. Explanation: Vector Comparison.

All the vectors below have the same magnitude. Is the magnitude of the sum of the two vectors on the left greater than, less than, or equal to the magnitude of the sum of the two vectors on the right? What could you draw to help explain your reasoning?
Tip.
This is a good activity to practice the steps in Figure 1.13.1.
Figure 1.12.3. A vector.

4. The Planets around the Sun.

Consider four of the planets distributed around the Sun: Earth, Mars, Jupiter, and Saturn. Suppose you want each planet to be able to send a message to any of the other planets.
Start by choosing any two planets. Your objective is to find the angle at which to direct the message from one planet to the other.
Begin by brainstorming what information you think would be useful to you in achieving this objective.
Below is information about the position of each planet relative to the Sun and an arbitrary positive axis starting at the Sun.
  • Earth: 1 AU from the Sun; 150 degrees left of the axis
  • Mars: 1.5 AU from the Sun; 90 degrees right of the axis
  • Jupiter: 5.2 AU from the Sun; 120 degrees left of the axis
  • Saturn: 9.5 AU from the Sun; 30 degrees right of the axis
Tip.
This is a good activity to practice the steps in Figure 1.5.9. In particular, consider how much work might be saved by solving for one pair of planets symbolically in contrast to solving for every pair of planets separately.
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