Position And Displacement Vectors In Two And Three Dimensions

This video tutorial explains position vectors and their use in calculating displacement vectors. It begins with an introduction to position vectors, followed by examples in both 2D and 3D coordinate systems. The tutorial demonstrates how to calculate the magnitude of a position vector and how to use position vectors to determine displacement vectors. The video concludes with information on additional resources available on the instructor's website.

What is a position vector?

• A vector that represents force

• A vector that points from one point to another

• A vector that starts from the origin and points to a specific point

• A vector that represents speed

How do you calculate the position vector for a point (3, 2) in a 2D space?

• 2i + 3j

• 3i + 2j

• 3j + 2i

• 2j + 3i

In a 3D coordinate system, what is the position vector for the point (3, 4, 5)?

• 3i + 5j + 4k

• 3i + 4j + 5k

• 4i + 3j + 5k

• 5i + 4j + 3k

What is the formula to find the magnitude of a position vector in 3D?

• √(x^2 + y^2 + z^2)

• x^2 + y^2 + z^2

• √(x^2 + y^2)

• x + y + z

Calculate the magnitude of the position vector (3, 4, 5).

• √100

• √75

• √25

• √50

What is a displacement vector?

• A vector that represents the change in position

• A vector that represents the change in velocity

• A vector that represents the change in acceleration

• A vector that represents the change in force

How do you calculate the displacement vector between two points A(2, 3, 4) and B(5, -2, 8)?

• 3i + 5j - 4k

• 3i + 5j + 4k

• 3i - 5j + 4k

• 3i - 5j - 4k

What is the displacement vector from point A(2, 3, 4) to point B(5, -2, 8)?

• 3i - 5j - 4k

• 3i + 5j + 4k

• 3i + 5j - 4k

• 3i - 5j + 4k

Which of the following is true about displacement vectors?

• They are the sum of two position vectors

• They are always positive

• They are the product of two position vectors

• They are the difference between two position vectors

Where can you find additional resources on position and displacement vectors?

• physics.tutor.edu

• science.tutor.org

• math.tutor.com

• video.tutor.net