Chapters

Three or more points are collinear if they are part of the same straight line and as a result the rank of the vectors is 1.

1.Determine if the points A = (2, 3, 1), B = (5, 4, 3) and C = (2, 1, 2) are collinear.

The points are not collinear.

## Midpoint

If A = (x_{1}, y_{1}, z_{1}) and B = (x_{2}, y_{2}, z_{2}) are the endpoints of a line segment, the midpoint of the line segment is given by:

1.Given the endpoints A = (3, −2, 5) and B = (3, 1, 7), find the coordinates of the midpoint of the line segment that they determine.

2.The coordinates of consecutive vertices of a parallelogram are A = (1, 0, 0) and B = (0, 1, 0). If the center coordinates of M are (0, 0, 1), find the coordinates of the vertices C and D.

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