Answer:
A) Non-collinear- does not lies on straight line
B) Collinear- lie on straight line
Step-by-step explanation:
We have to check collinearity of three points.
The points [tex](x_1, y_1, z_1),(x_2, y_2, z_2),(x_3, y_3, z_3)[/tex] are said to be collinear if,
[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]
A) A(2, 5, 3), B(3, 7, 1), C(1, 4, 4)
[tex]\left[\begin{array}{ccc}2&5&3\\3&7&1\\1&4&4\end{array}\right] \\\\=2(28-4)-5(12-1)+3(12-7)\\= 8 \neq 0[/tex]
Thus, the given points are not collinear.
B) D(0,-5,5), E(1,-2,4), F(3,4,2)
[tex]\left[\begin{array}{ccc}0&-5&5\\1&-2&4\\3&4&2\end{array}\right] \\\\=0(-4-16)+5(2-12)+5(4+6)\\=0[/tex]
Thus, the given points are collinear.
