If the vertices of a triangle be $(a, b - c)$ , $(c, - b, 0)$ and $(b, 0, c)$ , then the centroid of the triangle lies

at origin

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x

-axis

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y

-axis

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None of these

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Solution

The correct option is B on $x$ -axis
Given the vertices of a triangle be $(a, b - c)$ , $(c, - b, 0)$ and $(b, 0, c)$ .

Then the centroid of the triangle will be, $(\frac{a + c + b}{3}, \frac{b - b + 0}{3}, \frac{- c + 0 + c}{3})$ $= (\frac{a + c + b}{3}, 0, 0)$ .

Clearly the point lies on the $x$ axis.

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If the vertices of a triangle be (a,b−c), (c,−b,0) and (b,0,c), then the centroid of the triangle lies

The correct option is B on x-axisGiven the vertices of a triangle be (a,b−c), (c,−b,0) and (b,0,c).Then the centroid of the triangle will be, (a+c+b3,b−b+03,−c+0+c3)=(a+c+b3,0,0).Clearly the point lies on the x axis.

If the vertices of a triangle be $(a, b - c)$ , $(c, - b, 0)$ and $(b, 0, c)$ , then the centroid of the triangle lies