Question

Determine whether the points lie on straight line.

Answer 1

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 $(x_1, y_1, z_1),(x_2, y_2, z_2),(x_3, y_3, z_3)$ are said to be collinear if,

$\left[\begin{array}{ccc}x_1&y_1&z_1\\x_2&y_2&z_2\\x_3&y_3&z_3\end{array}\right] = 0$

A) A(2, 5, 3), B(3, 7, 1), C(1, 4, 4)

$\left[\begin{array}{ccc}2&5&3\\3&7&1\\1&4&4\end{array}\right] \\\\=2(28-4)-5(12-1)+3(12-7)\\= 8 \neq 0$

Thus, the given points are not collinear.

B) D(0,-5,5), E(1,-2,4), F(3,4,2)

$\left[\begin{array}{ccc}0&-5&5\\1&-2&4\\3&4&2\end{array}\right] \\\\=0(-4-16)+5(2-12)+5(4+6)\\=0$

Thus, the given points are collinear.