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
are said to be collinear if,
![\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](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx_1%26y_1%26z_1%5C%5Cx_2%26y_2%26z_2%5C%5Cx_3%26y_3%26z_3%5Cend%7Barray%7D%5Cright%5D%20%3D%200)
A) A(2, 5, 3), B(3, 7, 1), C(1, 4, 4)
![\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](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%265%263%5C%5C3%267%261%5C%5C1%264%264%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%3D2%2828-4%29-5%2812-1%29%2B3%2812-7%29%5C%5C%3D%208%20%5Cneq%200)
Thus, the given points are not collinear.
B) D(0,-5,5), E(1,-2,4), F(3,4,2)
![\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](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%26-5%265%5C%5C1%26-2%264%5C%5C3%264%262%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%3D0%28-4-16%29%2B5%282-12%29%2B5%284%2B6%29%5C%5C%3D0)
Thus, the given points are collinear.