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Question

If the centroid of triangle whose vertices are (a, 1, 3), (–2, b, –5) and (4, 7, c) is origin, then the value of c – a – b is _____
___

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Solution


Coordinates of centroid of the triangle is given by
G(x1+x2+x33,y1+y2+y33,z1+z2+z33)
Substituting the coordinates of triangle in the above relation, we get
G(a2+43,1+b+73,35+c3)
We are given centroid is the origin (0,0,0) .
a2+43=0,1+b+73=0 and 35+c3=0
a2+43=0a=2
1+b+73=0b=8
35+c3=0c=2
cab=2(2)(8)
=2+2+8
=12

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