# If the origin is the centroid of the triangle PQR with vertices P (2a, 2, 6), Q (– 4, 3b, –10) and R(8, 14, 2c), then find the values of a, b and c.

Given: The vertices of the triangle are P (2a, 2, 6), Q (-4, 3b, -10) and R (8, 14, 2c).

x1 = 2a, y1 = 2, z1 = 6; x2 = -4, y2 = 3b, z2 = -10; x3 = 8, y3 = 14, z3 = 2c

We know that the coordinates of the centroid of the triangle, whose vertices are (x1, y1, z1), (x2, y2, z2) and (x3, y3, z3), are .

So, the coordinates of the centroid of the triangle PQR are

Now, it is given that the origin (0, 0, 0) is the centroid.

So, we have

2a +4 = 0, 3b + 16 = 0, 2c 4 = 0

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Introduction To Cell Division60 mins
Introduction to Rotation & Torque37 mins
Introduction to Ionic Equilibrium48 mins
Introduction to Thermodynamics63 mins
Know All About Centroid of Triangle & its Properties56 mins
Introduction to Chemical Bonding63 mins
Everything you need to know about Orthocentre46 mins
Interactive Quiz on Centroid, incentre, orthocentre & circumcentre56 mins
Introduction to free body diagrams49 mins
Introduction to moment of inertia39 mins
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