Using section formula, show that the points A (2, –3, 4), B (–1, 2, 1) and are collinear - Maths - Introduction to Three Dimensional Geometry

Question

Using section formula, show that the points A (2, –3, 4),
B (–1, 2, 1) and are
collinear

Gopal Mohanty · Accepted Answer

The given points are A (2, –3, 4), B (–1, 2, 1), and

Let P be a point that divides AB in the ratio k:1 Hence, by section formula, the coordinates of P are given by

Now, we find the value of k at which point P coincides with point C By taking

, we obtain k = 2 For k = 2, the coordinates of point P are

i e ,

is a point that divides AB externally in the ratio 2:1 and is the same as point P Hence, points A, B, and C are collinear

Using section formula, show that the points A (2, –3, 4), B (–1, 2, 1) and are collinear.