Determining if 3 Points Lie on the Same Line Using the Cross Product
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In this video I go over a method for determining if 3 points lie on the same line by using the cross product of any 2 position vectors formed from the points. If the cross product is zero then the points all lie on the same line. This is because the cross product is also equal to the lengths of the position vectors multiplied by the sine of the angle between them. If the angle is zero, then sin(0) = 0 and so is the cross product equal to 0.
Timestamps:
- Question 16: Three points on a line: 0:00
- Solution to (a): Cross Product is zero if 2 vectors are on the same line: 0:17
- Illustration of the method: 1:15
- Cross product of position vectors is zero if they are on same line: 2:41
Full video and playlists:
- Full video:
- HIVE notes: https://peakd.com/hive-128780/@mes/vectors-and-the-geometry-of-space-review
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EMiATrjv8HH3fPwKVsgU6P
- Vectors and the Geometry of Space playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .
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