Three-Dimensional Coordinate Systems

The video tutorial introduces the three-dimensional coordinate system by adding the z-axis to the familiar XY plane, creating a space known as R3. It explains the concept of ordered triplets, which are used to define points in this space, and demonstrates how to plot these points by moving along the x, y, and z directions. The tutorial also covers the three main coordinate planes in 3D space: the XY, XZ, and YZ planes, each defined by setting one of the coordinates to zero. Finally, it discusses the division of 3D space into eight regions called octants, drawing parallels to the four quadrants of the XY plane.

What is the primary difference between a two-dimensional and a three-dimensional coordinate system?

• The removal of the x-axis

• The addition of the w-axis

• The removal of the y-axis

• The addition of the z-axis

How is an ordered triplet defined in a three-dimensional space?

• As YZ

• As XZ

• As XY

• As XYZ

What is the first step in plotting an ordered triplet in 3D space?

• Move out b units in the y-direction

• Move out a units in the x-direction

• Move out c units in the z-direction

• Move out d units in the w-direction

Which plane contains the x and y axes in three-dimensional space?

• YZ plane

• XZ plane

• ZW plane

• XY plane

What equation defines the XZ plane in three-dimensional space?

• y = 0

• z = 0

• x = 0

• w = 0

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

• Six

• Ten

• Eight

• Four

What is the defining characteristic of the first octant?

• All coordinates are negative

• X and Y are positive, Z is negative

• All coordinates are positive

• X is negative, Y and Z are positive

Where are the first four octants located in relation to the XY plane?

• Above the XY plane

• Below the XY plane

• On the XY plane

• Beside the XY plane

Which octants are located below the XY plane?

• 3rd and 4th octants

• 1st and 2nd octants

• 1st to 4th octants

• 5th to 8th octants

What direction does the negative Z-axis move in relation to the XY plane?

• Above the XY plane

• On the XY plane

• Beside the XY plane

• Below the XY plane