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If D, E, F be the middle points of the sides BC, CA and AB of the triangle ABC, then AD+BE+CF is
Asked by ohhnoaman | 25 Sep, 2023, 08:36: PM
answered-by-expert Expert Answer
To prove: AD + BE + CF = 0
Let space straight a with rightwards arrow on top comma space bold b with bold rightwards arrow on top comma space straight c with rightwards arrow on top comma space straight d with rightwards arrow on top comma space straight e with rightwards arrow on top comma space straight f with rightwards arrow on top space be space the space position space vectors space of space straight A comma space straight B comma straight C comma space straight D comma space straight E comma space straight F space respectively. rightwards double arrow straight d with rightwards arrow on top equals fraction numerator straight b with rightwards arrow on top plus straight c with rightwards arrow on top over denominator 2 end fraction comma space straight e with rightwards arrow on top equals fraction numerator straight c with rightwards arrow on top plus straight a with rightwards arrow on top over denominator 2 end fraction comma space straight f with rightwards arrow on top equals fraction numerator straight a with rightwards arrow on top plus straight b with rightwards arrow on top over denominator 2 end fraction rightwards double arrow AD with rightwards arrow on top plus BE with rightwards arrow on top plus CF with rightwards arrow on top equals open parentheses straight d with rightwards arrow on top minus straight a with rightwards arrow on top close parentheses plus open parentheses straight e with rightwards arrow on top minus straight b with rightwards arrow on top close parentheses plus open parentheses straight f with rightwards arrow on top minus straight c with rightwards arrow on top close parentheses equals open parentheses fraction numerator straight b with rightwards arrow on top plus straight c with rightwards arrow on top over denominator 2 end fraction minus straight a with rightwards arrow on top close parentheses plus open parentheses fraction numerator straight c with rightwards arrow on top plus straight a with rightwards arrow on top over denominator 2 end fraction minus straight b with rightwards arrow on top close parentheses plus open parentheses fraction numerator straight a with rightwards arrow on top plus straight b with rightwards arrow on top over denominator 2 end fraction minus straight c with rightwards arrow on top close parentheses rightwards double arrow AD with rightwards arrow on top plus BE with rightwards arrow on top plus CF with rightwards arrow on top equals 0
Answered by Renu Varma | 27 Sep, 2023, 04:37: PM

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If D, E, F be the middle points of the sides BC, CA and AB of the triangle ABC, then AD+BE+CF is
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