Finding Coordinates of Vertex C

The video tutorial explains how to determine the coordinates of the vertices of a parallelogram defined in R3 by vectors AO and OB. It involves sketching the parallelogram, labeling the points, and using vector addition to find the unknown vertex C. The process includes equating vectors OA and BC to solve for the coordinates of C, resulting in the final answer for the given problem.

What is the main objective of the problem discussed in the video?

• To find the area of a parallelogram

• To find the angles of a parallelogram

• To calculate the perimeter of a parallelogram

• To determine the coordinates of the vertices of a parallelogram

What is the first step suggested for solving the problem?

• Sketch a parallelogram

• Calculate the area

• Find the midpoint

• Determine the angles

What are the coordinates of vertex A?

• (3, 2, 0)

• (1, 2, 4)

• (4, 4, 4)

• (0, 0, 0)

What are the coordinates of vertex B?

• (3, 2, 0)

• (1, 2, 4)

• (0, 0, 0)

• (4, 4, 4)

What is the unknown vertex we need to find?

• Vertex C

• Vertex A

• Vertex B

• Vertex D

What property of parallelograms is used to find vertex C?

• Opposite sides are parallel

• All angles are right angles

• Opposite sides are equal

• Diagonals bisect each other

What is the equation derived for the x-coordinate of vertex C?

• x - 1 = 3

• x + 1 = 3

• x - 2 = 3

• x + 2 = 3

What is the x-coordinate of vertex C?

• 5

• 3

• 4

• 6

What is the y-coordinate of vertex C?

• 5

• 4

• 3

• 2

What is the z-coordinate of vertex C?

• 2

• 3

• 4

• 5