Home
Class 10
MATHS
If the centroid of the triangle formed b...

If the centroid of the triangle formed by the points (a,b) , (b,c) and (c,a) is at the origin, then find the value of `a^3+b^3+c^3`.

Text Solution

Verified by Experts

Centroid of the given triangle will be `((a+b+c)/3,(b+c+a)/3).`
We are given, centroid is at the origin.
`:. (a+b+c)/3 = 0 and (b+c+a)/3 = 0`
`=>a+b+c = 0`
We know,
`a^3+b^3+c^3-3abc = (a+b+c)(a^2+b^2+c^2-ab-bc-ca)`
Here, `a+b+c = 0`,
`:. a^3+b^3+c^3-3abc = 0`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

If the centroid of the triangle formed by points P(a,b),Q(b,c) and R(c,a) is at the origin, what is the value of a+b+c?

If the centroid of the triangle formed by points P(a ,\ b),\ \ Q(b ,\ c) and R(c ,\ a) is at the origin, what is the value of a+b+c ?

If the centroid of the triangle formed by points P ( a , b ) , Q ( b , c ) and R ( c , a ) is at the origin, what is the value of (a^2)/(b c)+(b^2)/(c a)+(c^2)/(a b) ?

If the centroid of the triangle formed by points P ( a , b ) , Q ( b , c ) and R ( c , a ) is at the origin, what is the value of a + b + c ? In Q. No. 169, what is the value of (a^2)/(b c)+(b^2)/(c a)+(c^2)/(a b) ?

If the centroid of the triangle formed by the points (a ,\ b),\ (b ,\ c) and (c ,\ a) is at the origin, then a^3+b^3+c^3= a b c (b) 0 (c) a+b+c (d) 3\ a b c

The area of the triangle formed by the points (a, b+c), (b, c+a), (c, a+b) is

The area of the triangle formed by the points (a,b+c),(b,c+a),(c,a+b) is

If the centroid of a triangle formed by the points a. b), (b, c), and (c a) is at the origin, then a^(3) + b^(3) + c^(3) =

If the centroid of the triangle formed by the points (a,b),(b,c) and (c,a) is at the origin,then a^(3)+b^(3)+c^(3)=abc(b)0(c)a+b+c(d)3abc

If the centroid of the triangle formed by (a,1,3) ,(-2,b,-5) and (4,7,c) is the origin then (a,b,c) =