3D Coordinate System and Applications

The video tutorial introduces the 3D coordinate system, explaining the x, y, and z axes. It covers plotting points in 3D, understanding planes and octants, and calculating distances and midpoints. The tutorial also explains how to formulate equations for spheres and find diagonal lengths in 3D objects, providing a comprehensive overview of basic 3D geometry concepts.

In the 3D coordinate system, which axis runs parallel to a tabletop from front to back?

• w-axis

• y-axis

• x-axis

• z-axis

What is the name of the plane where the z-coordinate is zero?

• XZ plane

• YZ plane

• XY plane

• ZX plane

In the first octant of the 3D coordinate system, what are the signs of the x, y, and z coordinates?

• Positive, Positive, Positive

• Positive, Positive, Negative

• Negative, Positive, Positive

• Negative, Negative, Positive

Which octant has all negative coordinates?

• Octant 6

• Octant 5

• Octant 7

• Octant 8

When plotting a point with coordinates (2, -3, 3) in 3D, which direction do you move for the y-coordinate?

• Down

• Right

• Left

• Up

What additional component is added to the 2D distance formula to adapt it for 3D?

• Difference of x squared

• Difference of y squared

• Sum of all coordinates

• Difference of z squared

How do you find the midpoint between two points in 3D space?

• Add x, y, z and divide by 3

• Add x, y, z and divide by 2

• Add x, y, z and divide by 5

• Add x, y, z and divide by 4

What is the equation of a sphere in standard form?

• (x-h)^2 + (y-k)^2 + (z-j)^2 = r^2

• x^2 + y^2 + z^2 = r^2

• x^2 + y^2 = r^2

• (x-h)^2 + (y-k)^2 = r^2

To convert a sphere's equation to standard form, what mathematical process is used?

• Completing the square

• Differentiation

• Integration

• Factoring

If a sphere's center is at the origin, what is the simplified form of its equation?

• (x-h)^2 + (y-k)^2 = r^2

• (x-h)^2 + (y-k)^2 + (z-j)^2 = r^2

• x^2 + y^2 = r^2

• x^2 + y^2 + z^2 = r^2