Calculus III: Three Dimensional Coordinate Systems (Level 6 of 10)

The video covers three complex problems using the 3D distance formula. It starts with analyzing triangle PQR to determine its type, then finds points on a line perpendicular to the XY plane at a specific distance from another point. Finally, it identifies a point on the Y-axis equidistant from two given points.

Which condition must be met for a triangle to be classified as equilateral?

• Two sides are of equal length.

• All angles are equal.

• All sides are of equal length.

• All sides are of different lengths.

How can you verify if a triangle is a right triangle using side lengths?

• Check if all sides are equal.

• Calculate the area of the triangle.

• Use the Pythagorean theorem.

• Ensure two sides are equal.

What is the first step in using the distance formula in three dimensions?

• Identify the coordinates of the points.

• Calculate the area of the triangle.

• Determine the type of triangle.

• Find the midpoint of the line segment.

What is the significance of a line being perpendicular to the xy-plane?

• It forms a right angle with the xy-plane.

• It is parallel to the xy-plane.

• It intersects the xy-plane at multiple points.

• It lies entirely on the xy-plane.

When a line is perpendicular to the xy-plane, which coordinates remain constant?

• All coordinates change

• y and z coordinates

• x and z coordinates

• x and y coordinates

What is the result when solving for z in the second example?

• z = 5 and z = -5

• z = 11 and z = -1

• z = 7 and z = -7

• z = 3 and z = -3

In the final example, what is the x-coordinate of the point on the y-axis?

• 0

• 2

• 3

• 1

What is the y-coordinate of the point equidistant from two given points in the final example?

• 6

• 3

• 5

• 4

Which formula is used to find the distance between two points in three dimensions?

• Slope formula

• Distance formula

• Midpoint formula

• Area formula

What topic will be covered in the next video?

• Equation of a line

• Properties of triangles

• Distance formula in two dimensions

• Equation of a sphere