Use vectors to determine whether the points are collinear. (-3,-3,7), (2,-4,6), (1,-4,5)
A)not collinear
B)collinear

Question

Quizplus · Accepted Answer

To determine if the points are collinear, we need to check if they all lie on the same line. We can use vectors to do this. If we find that the vectors connecting any two of the three points are linearly dependent, then the points are collinear.

Let's start by finding the vectors:

v1 = (2-(-3), -4-(-3), 6-7) = (5, -1, -1)
v2 = (1-(-3), -4-(-3), 5-7) = (4, -1, -2)

Now let's check if they are linearly dependent by taking their cross product:

v1 x v2 = det | i     j      k |
| 5  -1  -1 |
| 4  -1  -2 | = (-1i + 6j + 1k)

Since the cross product is not the zero vector, the vectors v1 and v2 are linearly independent. Therefore, the points (-3,-3,7), (2,-4,6), (1,-4,5) are not collinear.

Use Vectors to Determine Whether the Points Are Collinear