ABCDE is a pentagon- If the sum of the vectors AB-AE-BC-DC-ED and AC is - AC- then find the value of -

In ABC,A⃗B⃗+B⃗C⃗+C⃗A⃗=0A⃗B⃗+B⃗C⃗=A⃗C⃗ In quadrilateral AEDC,A⃗E⃗+E⃗D⃗+D⃗C⃗+C⃗A⃗=0A⃗E⃗+E⃗D⃗+D⃗C⃗=A⃗C⃗ A⃗B⃗+B⃗C⃗+A⃗E⃗+E⃗D⃗+D⃗C⃗+A⃗C⃗ =A⃗C⃗+A⃗C⃗+A⃗C ...

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Addition of vectors

ABCDE is a pe...

Question

$A B C D E$ is a pentagon. If the sum of the vectors $A B, A E, B C, D C, E D$ and $A C$ is $λ$ $A C$ , then find the value of $λ$ .

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A B C D E

\to A B + \to A E + \to B C + \to D C + \to E D + \to A C

A B C D E

\to A B + \to B C + \to D C + \to E D + \to A E = k \to A C

k

\vec{A B} + \vec{B C} + \vec{C D} + \vec{D E} + \vec{E A} = \vec{0}

\vec{A B} + \vec{A E} + \vec{B C} + \vec{D C} + \vec{E D} + \vec{A C} = 3 \vec{A C}

A B C D E

A B = A E, B C = E D

∠ A B C = ∠ A E D .

A C = A D

- - \to A B + - - \to A C + - - \to A D + - - \to A E + - - \to A F = λ - - \to A D

λ

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