Name: Jakob Date:
Student Exploration: Vectors
Directions: Follow the instructions to go through the simulation. Respond to the questions and
prompts in the orange boxes.
Vocabulary: component, magnitude, resultant, scalar, unit vector notation, vector
Prior Knowledge Question (Do this BEFORE using the Gizmo.)
An airplane is traveling north at 300 km/h. Suddenly, it is hit by a strong
crosswind blowing 150 km/h from west to east.
Draw an arrow on the diagram showing the direction you think the
plane will most likely move. Explain your answer.
The plane will continue to move forward because there is a slight
wind moving east, and the plane would slightly go northeast
Gizmo Warm-up
Displacement, velocity, momentum, acceleration, and force are all
examples of quantities that have both direction and magnitude.
Anything with direction and magnitude can be represented using a
vector.
Look at vectors a and b on the Vectors Gizmo grid. The initial point of
each vector is shown with a circle. The terminal point of each vector is
located at the tip of the arrow. Each vector is described by two
components: the i component and the j component.
1. The two components written together make up the unit vector notation. What is the unit vector notation of
vector a?
-2i+4j
2. Move the initial point of vector a to the origin (0, 0) on the grid.
A. How did the components of vector a change? No they didn’t change
B. Drag the terminal point of vector a so that it lines up with the x-axis. Which component
describes the vector’s position along the x-axis? i
C. Drag the terminal point of a so that it lines up with the y-axis. Which component describes the
vector’s position along the y-axis? j
Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved
, Activity A: Get the Gizmo ready:
Vector magnitude ● Change vector a so that its notation is 0i + 3j.
and angle ● You will need a scientific calculator for this activity.
Question: How can you determine a vector’s magnitude and angle?
1. Observe: The magnitude of a vector is the distance from the vector’s initial point to its terminal point. The
magnitude of a vector is written: ||x||. Magnitude is a scalar, or a number that does not indicate direction.
A. What is the magnitude of vector a? ||a|| = 3
Turn on Show ruler and use the ruler to check your answer.
B. Turn off the ruler. Drag the tip of vector a so that its notation is 4i + 3j. What do you
think the magnitude of vector a is now? ||a|| = 5
2. Explore: A vector can be broken down into perpendicular vectors that describe its length along the x and y
axes. Turn on Show x, y components. How do the x and y vectors that appear for vector a relate to the i
and j notation?
The x vector represents the i portion of the vector notation and the y represents the j
portion of the horizontal notation
3. Calculate: The x, y components of vector a form the two sides of a right triangle. The length of the
hypotenuse of that triangle will equal the length (and, thus, the magnitude) of vector a.
The Pythagorean theorem states that for a right triangle, the square of the hypotenuse equals the sum of
the squares of the other two sides:
(length of hypotenuse)2 = (length of one side)2 + (length of other side)2
Use the Pythagorean theorem to calculate the magnitude of vector a.
||a|| = 5
Turn on Show ruler and use the ruler to check your answer.
4. Apply: What are the magnitudes of the following vectors?
||3i – 5j|| = 5.83 ||–1i – 2j|| = 2.24 ||–14i + 3j|| = 14.32
Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved
Student Exploration: Vectors
Directions: Follow the instructions to go through the simulation. Respond to the questions and
prompts in the orange boxes.
Vocabulary: component, magnitude, resultant, scalar, unit vector notation, vector
Prior Knowledge Question (Do this BEFORE using the Gizmo.)
An airplane is traveling north at 300 km/h. Suddenly, it is hit by a strong
crosswind blowing 150 km/h from west to east.
Draw an arrow on the diagram showing the direction you think the
plane will most likely move. Explain your answer.
The plane will continue to move forward because there is a slight
wind moving east, and the plane would slightly go northeast
Gizmo Warm-up
Displacement, velocity, momentum, acceleration, and force are all
examples of quantities that have both direction and magnitude.
Anything with direction and magnitude can be represented using a
vector.
Look at vectors a and b on the Vectors Gizmo grid. The initial point of
each vector is shown with a circle. The terminal point of each vector is
located at the tip of the arrow. Each vector is described by two
components: the i component and the j component.
1. The two components written together make up the unit vector notation. What is the unit vector notation of
vector a?
-2i+4j
2. Move the initial point of vector a to the origin (0, 0) on the grid.
A. How did the components of vector a change? No they didn’t change
B. Drag the terminal point of vector a so that it lines up with the x-axis. Which component
describes the vector’s position along the x-axis? i
C. Drag the terminal point of a so that it lines up with the y-axis. Which component describes the
vector’s position along the y-axis? j
Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved
, Activity A: Get the Gizmo ready:
Vector magnitude ● Change vector a so that its notation is 0i + 3j.
and angle ● You will need a scientific calculator for this activity.
Question: How can you determine a vector’s magnitude and angle?
1. Observe: The magnitude of a vector is the distance from the vector’s initial point to its terminal point. The
magnitude of a vector is written: ||x||. Magnitude is a scalar, or a number that does not indicate direction.
A. What is the magnitude of vector a? ||a|| = 3
Turn on Show ruler and use the ruler to check your answer.
B. Turn off the ruler. Drag the tip of vector a so that its notation is 4i + 3j. What do you
think the magnitude of vector a is now? ||a|| = 5
2. Explore: A vector can be broken down into perpendicular vectors that describe its length along the x and y
axes. Turn on Show x, y components. How do the x and y vectors that appear for vector a relate to the i
and j notation?
The x vector represents the i portion of the vector notation and the y represents the j
portion of the horizontal notation
3. Calculate: The x, y components of vector a form the two sides of a right triangle. The length of the
hypotenuse of that triangle will equal the length (and, thus, the magnitude) of vector a.
The Pythagorean theorem states that for a right triangle, the square of the hypotenuse equals the sum of
the squares of the other two sides:
(length of hypotenuse)2 = (length of one side)2 + (length of other side)2
Use the Pythagorean theorem to calculate the magnitude of vector a.
||a|| = 5
Turn on Show ruler and use the ruler to check your answer.
4. Apply: What are the magnitudes of the following vectors?
||3i – 5j|| = 5.83 ||–1i – 2j|| = 2.24 ||–14i + 3j|| = 14.32
Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved
