Solveeit Logo
Login

Question

Question: If \(D,E,F\) are respectively the mid points of \(AB,AC\)and \(BC\) in \(\Delta ABC\), then \(\overs...

If D,E,FD,E,F are respectively the mid points of AB,ACAB,ACand BCBC in ΔABC\Delta ABC, then BE→+AF→=\overset{\rightarrow}{BE} + \overset{\rightarrow}{AF} =

A

DC→\overset{\rightarrow}{DC}

B

12BF→\frac{1}{2}\overset{\rightarrow}{BF}

C

2BF→2\overset{\rightarrow}{BF}

D

32BF→\frac{3}{2}\overset{\rightarrow}{BF}

Answer

DC→\overset{\rightarrow}{DC}

Explanation

Solution

BE→+AF→=OE→−OB→+OF→−OA→\overset{\rightarrow}{BE} + \overset{\rightarrow}{AF} = \overset{\rightarrow}{OE} - \overset{\rightarrow}{OB} + \overset{\rightarrow}{OF} - \overset{\rightarrow}{OA}

=OA→+OC→2−OB→+OB→+OC→2−OA→= \frac{\overset{\rightarrow}{OA} + \overset{\rightarrow}{OC}}{2} - \overset{\rightarrow}{OB} + \frac{\overset{\rightarrow}{OB} + \overset{\rightarrow}{OC}}{2} - \overset{\rightarrow}{OA}

=OC→−OA→+OB→2=OC→−OD→=DC→= \overset{\rightarrow}{OC} - \frac{\overset{\rightarrow}{OA} + \overset{\rightarrow}{OB}}{2} = \overset{\rightarrow}{OC} - \overset{\rightarrow}{OD} = \overset{\rightarrow}{DC}.