Find the vectors from the origin to the intersection of the medians of the triangle whose vertices are A(5,2,1), B(-4,7,0) and C(5, -3,5)

Explanation

Given that A = (5,2,1), B = (-4,7,0)
C = (5,-3,5)
Then position vectors of A, B, C are
`5hat+2hatj`, `-4hati+7hatj`. `5hati-3hatj+5hatk` respectively
Let G be the point of intersection of the medians of the triangle ABC.
Then the position of vector G
= `((5hati+2hatj+hatk) + (-4hati+7hatj) + (5hati-3hatj+5hatk))/3`
`(6hati+6hatj+6hatk)/3` = `2hati+2hatj+2hatk`