Let D- E- F be the mid points of the sides BC- CA- AB respectively of a - ABC- Then-AD-BE-CF equals

Let the position vectors of A, B, C be a⃗, b⃗ and c⃗ Then the position vectors of D, E and F are b⃗+c⃗/2, c⃗+a⃗/2 and a⃗+b⃗/2 respectively. Therefore, AD+BE+CF ...

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Byju's Answer

Standard XIII

Mathematics

Addition of Vectors

Let D, E, F b...

Question

Let D, E, F be the mid points of the sides BC, CA, AB respectively of a $Δ A B C$ . Then, $- - \to A D + - - \to B E + - - \to C F$ equals

\to 0

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2 - - \to A B

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3 - - \to A B

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5 - - \to A B

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Solution

The correct option is A $\to 0$
Let the position vectors of A, B, C be $\to a, \to b$ and $\to c$ Then the position vectors of D, E and F are $\frac{\to b + \to c}{2}, \frac{\to c + \to a}{2}$ and $\frac{\to a + \to b}{2}$ respectively. Therefore, $- - \to A D + - - \to B E + - - \to C F$
$= (\frac{\to b + \to c}{2} - \to a) + (\frac{\to c + \to a}{2} - \to b) + (\frac{\to a + \to b}{2} - \to c) = \to 0$

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Let D, E, F be the mid points of the sides BC, CA, AB respectively of a ΔABC. Then,−−→AD+−−→BE+−−→CF equals

The correct option is A →0Let the position vectors of A, B, C be →a,→b and →c Then the position vectors of D, E and F are →b+→c2,→c+→a2 and →a+→b2 respectively. Therefore, −−→AD+−−→BE+−−→CF =(→b+→c2−→a)+(→c+→a2−→b)+(→a+→b2−→c)=→0

Let D, E, F be the mid points of the sides BC, CA, AB respectively of a $Δ A B C$ . Then, $- - \to A D + - - \to B E + - - \to C F$ equals