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Show that the point A (1,-1,3), B ( 2,-...

Show that the point A (1,-1,3), B ( 2,-4,5) and C ( 5,-13,11) are collinear.

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AI Generated Solution

To show that the points A(1, -1, 3), B(2, -4, 5), and C(5, -13, 11) are collinear, we can use the concept of vectors. Specifically, we will find the vectors AB and AC and check if they are scalar multiples of each other. If they are, then the points are collinear. ### Step 1: Find the vectors AB and AC The vector AB can be calculated as follows: \[ \text{AB} = B - A = (2 - 1, -4 - (-1), 5 - 3) = (1, -3, 2) \] ...
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