9.3, Points in 3rd Dimension

What are the coordinates of a point in 3D space?

• The coordinates of a point in 3D space are represented as (a, b, c).

• The coordinates of a point in 3D space are represented as (x, y, z).

• The coordinates of a point in 3D space are represented as (x, y, w).

• The coordinates of a point in 3D space are represented as (1, 2, 3, 4).

How many axes are there in 3D space?

• 6

• 3

• 4

• 5

What is the name of the point where all three axes intersect in 3D space?

• origin

• junction

• center

• vertex

Explain the concept of distance between two points in 3D space.

• The distance between two points (x1, y1, z1) and (x2, y2, z2) in 3D space is given by sqrt((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)

• The distance between two points in 3D space is given by multiplying their coordinates

• The distance between two points in 3D space is always a negative value

• The distance between two points in 3D space is not affected by the difference in their z-coordinates

What is the formula to calculate the distance between two points in 3D space?

• sqrt(-(x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)

• sqrt((x2 - x1)^2 - (y2 - y1)^2 + (z2 - z1)^2)

• sqrt((x2 - x1)^2 + (y2 - y1)^2 - (z2 - z1)^2)

• sqrt((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)

Describe how to find the midpoint of a line segment in 3D space.

• The midpoint of a line segment in 3D space is found by averaging the x, y, and z coordinates of the two endpoints.

• The midpoint is determined by connecting the endpoints with a straight line.

• The midpoint is located at the endpoint with the highest z-coordinate.

• The midpoint is found by multiplying the coordinates of the two endpoints.

What are the three coordinates needed to represent a point in 3D space?

• x, y, z

• latitude, longitude, altitude

• a, b, c

• red, green, blue

Explain the concept of vectors in 3D space.

• Vectors in 3D space are quantities with magnitude and direction represented by ordered sets of three numbers (x, y, z).

• Vectors in 3D space have only magnitude, not direction.

• Vectors in 3D space are represented by two numbers instead of three.

• Vectors in 3D space are one-dimensional quantities.

How are vectors represented in 3D space?

• Vectors in 3D space are represented using their endpoints in a 3D coordinate system.

• Vectors in 3D space are represented using their components along the x and y axes.

• Vectors in 3D space are represented using their components along the x, y, and z axes.

• Vectors in 3D space are represented using their magnitude and direction only.

What is the dot product of two vectors in 3D space?

• The dot product of two vectors in 3D space is equal to the cross product of their magnitudes

• The dot product of two vectors in 3D space is equal to the product of their magnitudes

• The dot product of two vectors in 3D space is equal to the sum of the products of their respective components: A · B = Ax * Bx + Ay * By + Az * Bz

• The dot product of two vectors in 3D space is equal to the square of the sum of their components