Question

show that the points A(-7,4,-2), B(-2,1,0) and C(3,-2,2) are collinear​

Answer 1

Answer:

The three points A(-7,4,-2), B(-2,1,0) and C(3,-2,2) are collinear.

Step-by-step explanation:

We are given three points in the question:

A(-7,4,-2), B(-2,1,0) and C(3,-2,2)

If the area of triangle formed by these points is zero, then, the three points are collinear.

Thus, if the determinant of the three vertices is zero, then, the points are collinear.

$$\begin{lgathered}\left[\begin{array}{ccc}-7&4&-2\\-2&1&0\\3&-2&2\end{array}\right] \\\\=-7(2-0) -4(-4-0) -2(4-3)\\=-7(2) -4(-4) -2(1) \\= 0\end{lgathered}$$

Thus, the three points A(-7,4,-2), B(-2,1,0) and C(3,-2,2) are collinear.