{\ABCD} is a rhombus whose diagonals intersect at E. Then { {\EA}}^{\to}+{ {\EB}}^{\to}+{ {\EC}}^{\to}+ { {\ED}}^{\to} equals

CBSE Class 12 Math 2020 Delhi Set 1 Solved Paper - Question 6

Question : 6 of 36

Marks: +1, -0

{\ABCD}

is a rhombus whose diagonals intersect at E. Then

{ {\EA}}↖{→}+{ {\EB}}↖{→}+{ {\EC}}↖{→}+

{ {\ED}}↖{→}

equals

Solution:

Given

{\ABCD}

is a rhombus and diagonals intersect at

{\E}

Since in a rhombus diagonals bisect each other

|{ {\EA}}↖{→}|=|{ {\EC}}↖{→}| \;\text " and "\;|{ {\EB}}↖{→}|=|{ {\ED}}↖{→}|

but since they are opposite to each other they are of opposite signs

⇒ { {\EA}}↖{→}=-{ {\EC}}↖{→}

and

{ {\EB}}↖{→}=-{ {\ED}}↖{→}

⇒ { {\EA}}↖{→}+{ {\EC}}↖{→}={ {\O}}↖{→}

...(i) and

{ {\EB}}↖{→}+{ {\ED}}↖{→}={ {\O}}↖{→}

Add (1) and (2)

⇒ { {\EA}}↖{→}+{ {\EB}}↖{→}+{ {\EC}}↖{→}+{ {\ED}}↖{→}={ {\O}}↖{→}

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