Answer:
Condition for collinearity of three points on a line.
Step-by-step explanation:
We are given the following information in the question:
Point X, Y and Z lies on a line m.
We have to show that these points are collinear. Three points on a point are collinear if the area of triangle formed by these three points is zero.
We make the following assumptions.
Let [tex](x_1, y_1, z_1), (x_2, y_2, z_2), (x_3, y_3, z_3),[/tex] be the coordinates of point X, Y and Z respectively.
Then the area of triangle formed by these three points is given by:
[tex]\frac{1}{2}\left[\begin{array}{ccc}x_1&y_1&z_1\\x_2&y_2&z_2\\x_3&y_3&z_3\end{array}\right] }[/tex]
Equating area of triangle to zero,
[tex]\left[\begin{array}{ccc}x_1&y_1&z_1\\x_2&y_2&z_2\\x_3&y_3&z_3\end{array}\right] } = 0[/tex]
Hence, the above condition is the condition foe collinearity of three points on a given line.
