Answer :

Let the point P divides AB in the ratio k : 1.


Comparing this information with the details given in the question, we have

x1 = 2, y1 = -3, z1 = 4; x2 = -1, y2 = 2, z2 = 1 and m = k, n = 1

By section formula,

We know that the coordinates of the point R which divides the line segment joining two points P (x1, y1, z1) and Q (x2, y2, z2) internally in the ratio m : n is given by:

So, we have,

The coordinates of P =

Now, we check if for some value of k, the point coincides with the point C.


-k + 2 = 0 k = 2

When k =2, then


Therefore, C is a point which divides AB in the ratio 2 : 1 and is same as P.

Hence, A, B, C are collinear.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses

The ratio in whicRD Sharma - Mathematics

The ratio in whicRD Sharma - Mathematics

If a parallelepipRD Sharma - Mathematics

Two vertices of aRS Aggarwal - Mathematics

If the origin is RS Aggarwal - Mathematics

If the three consRS Aggarwal - Mathematics

Find the ratio inRD Sharma - Mathematics

Write the coordinRD Sharma - Mathematics

Find the coordinaRD Sharma - Mathematics

Find the centroidRD Sharma - Mathematics