3D Coordinate System Concepts

The video tutorial introduces the three-dimensional coordinate system, explaining its axes and orientation. It demonstrates how to plot points in 3D using coordinates and provides examples. The tutorial then introduces vectors, specifically position vectors, and explains how to calculate their length using the Pythagorean theorem. The video concludes by showing how to determine the distance from a point to the origin.

What are the three axes in a three-dimensional coordinate system?

• a, b, c

• 1, 2, 3

• p, q, r

• x, y, z

In the typical orientation of a 3D coordinate system, which direction does the z-axis point?

• Right

• Left

• Down

• Up

How do you determine the z-coordinate when plotting a point in 3D?

• Move up

• Move right

• Move left

• Move down

What are the coordinates of point B in the example given?

• 1, 2, 5

• 2, 4, 6

• 4, 6, 2

• 3, 5, 7

What is a position vector in a 3D coordinate system?

• A vector parallel to the y-axis

• A vector parallel to the x-axis

• A vector from the origin to a point

• A vector from point A to B

What are the components of a position vector?

• p, q, r

• 1, 2, 3

• x, y, z

• a, b, c

How is the length of a position vector calculated?

• Using the difference of coordinates

• Using the product of coordinates

• Using the Pythagorean theorem

• Using the sum of coordinates

What is the length of vector OA in the XY plane?

• x * y

• x^2 + y^2

• x + y

• x^2 - y^2

What does the magnitude of a position vector represent?

• The distance from the origin

• The angle of the vector

• The direction of the vector

• The speed of the vector

What is the formula for the magnitude of a position vector?

• x * y * z

• x^2 + y^2 + z^2

• sqrt(x^2 + y^2 + z^2)

• x + y + z