Question

If D, E, F are the mid points of the sides BC, CA and AB respectively of a triangle ABC and 'O' is any point, then, `|vec(AD) + vec(BE) + vec(CF)|`, is ______.

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Answer 1

If D, E, F are the mid points of the sides BC, CA and AB respectively of a triangle ABC and 'O' is any point, then, `|vec(AD) + vec(BE) + vec(CF)|`, is 0.

Explanation:

`vec(AD) + vec(BE) + vec(CF)`

= `((vecb + vecc)/2 - veca) + ((veca + vecc)/2 - vecb) + ((veca + vecb)/2 - vecc)`

= `(veca + vecb + vecc) - (veca + vecb + vecc)`

= 0

Hence `|vec(AD) + vec(BE) + vec(CF)|` = 0