Three-Dimensional Coordinate System Concepts

This video introduces the basics of 3D coordinate systems, including plotting points and understanding coordinate planes like XY, XZ, and YZ. It covers graphing equations in both 2D and 3D, explaining how to visualize and plot them. The video also discusses 3D inequalities and their 2D-3D analogues, and concludes with the distance formula in 3D and the equations of spheres.

What is required to describe the location of a point in a three-dimensional coordinate system?

• A vector

• A single coordinate

• An ordered triple (X, Y, Z)

• An ordered pair (X, Y)

In a right-hand-rule system, which direction does the positive Z-axis point?

• Downwards

• Towards the right

• Towards the left

• Upwards

What is the equation of the XY plane in a three-dimensional coordinate system?

• X + Y = 0

• Y = 0

• X = 0

• Z = 0

How many octants are there in a three-dimensional coordinate system?

• Four

• Six

• Eight

• Ten

When plotting the point (3, 2, 5) in 3D, how many units do you move in the Z direction?

• 3 units

• 5 units

• 7 units

• 2 units

What does the graph of x = 2 represent in 3D space?

• A point

• A curve

• A plane

• A line

In 3D space, what does the equation y = x represent?

• A plane

• A sphere

• A parabola

• A line

What is the shape of the graph of y = x^2 in 3D space?

• A line

• A plane

• A paraboloid

• A sphere

What does the inequality x ≤ y represent in 3D space?

• A line

• A region

• A plane

• A point

What additional term is added to the 2D distance formula to extend it to 3D?

• x2 - x1

• y2 - y1

• z2 - z1

• w2 - w1