Mystery Scalar and Vectors Investigation

Tim Brzezinski, May 27, 2020

Two vectors and a mystery scalar: Discovery Learning Investigation

Table of Contents

  1. What do You Notice?
    1. Mystery Scalar Exploration (Part 1)
  2. Diving Deeper
    1. Mystery Scalar Exploration (Part 2)
    2. Mystery Scalar Exploration (Part 3)
    3. Mystery Scalar Exploration (Part 4)
  3. More Specifics
    1. Mystery Scalar Exploration (Part 5)
    2. Mystery Scalar Exploration (Part 6)
  4. Any Connections?
    1. Mystery Scalar Exploration (Part 7)
    2. Mystery Scalar Exploration (Part 8)
    3. Mystery Scalar Exploration (Part 9)

1.

What do You Notice?

  • 1. Mystery Scalar Exploration (Part 1)

1.1.

Mystery Scalar Exploration (Part 1)

Move points A, B, and C around. As you do, pay close attention to the mystery number in the upper left corner.
What do you notice? What do you wonder? List/describe any observations.
– Tim Brzezinski

2.

Diving Deeper

  • 1. Mystery Scalar Exploration (Part 2)
  • 2. Mystery Scalar Exploration (Part 3)
  • 3. Mystery Scalar Exploration (Part 4)

2.1.

Mystery Scalar Exploration (Part 2)

Move points A, B, and C around. Use the tools of GeoGebra to help further explore any observation(s) you made in Part 1.
Any observations? Is there any relationship between the value of the mystery number and the position of the vectors?
– Tim Brzezinski

2.2.

–

2.3.

–

3.

More Specifics

  • 1. Mystery Scalar Exploration (Part 5)
  • 2. Mystery Scalar Exploration (Part 6)

3.1.

Mystery Scalar Exploration (Part 5)

In the app below, move the points around so both vectors shown have magnitude = 5.
When both vectors have magnitude = 5, is there a highest possible value of the mystery number? If so, what is it?
When both vectors have magnitude = 5, is there a lowest possible value of the mystery number? If so, what is it? [br]
– Tim Brzezinski

3.2.

–

4.

Any Connections?

  • 1. Mystery Scalar Exploration (Part 7)
  • 2. Mystery Scalar Exploration (Part 8)
  • 3. Mystery Scalar Exploration (Part 9)

4.1.

Mystery Scalar Exploration (Part 7)

This mystery number is called the [b]DOT PRODUCT[/b] of both vectors. [br][br]If 2 vectors have the same initial point, what can we conclude about their [b]dot product[/b]? List everything you have observed in the previous activities:
– Tim Brzezinski

4.2.

–

4.3.

–

Information