Use vectors to determine whether the points are collinear. (5,3,-5), (9,1,-1), (-11,11,-21)
A)collinear
B)not collinear

Question

Quizplus · Accepted Answer

To determine if the points are collinear, we can check if the vectors formed by these points are parallel. Let's take the points $P_1 = (5,3,-5)$, $P_2 = (9,1,-1)$, and $P_3 = (-11,11,-21)$. We form two vectors, $\vec{P_1P_2}$ and $\vec{P_1P_3}$, and then check if they are scalar multiples of each other.$\vec{P_1P_2} = P_2 - P_1 = (9-5, 1-3, -1+5) = (4, -2, 4)$$\vec{P_1P_3} = P_3 - P_1 = (-11-5, 11-3, -21+5) = (-16, 8, -16)$We can see that $\vec{P_1P_3} = -4 \times \vec{P_1P_2}$, indicating that these vectors are parallel and thus the points are collinear.

Use Vectors to Determine Whether the Points Are Collinear