Physics, asked by jeet8875, 1 year ago

ABCDE is a pentagon.Prove that vectors AB + BC + CD + CE + DE + EA = 0

Answers

Answered by mindfulmaisel
40

Let us consider a pentagon like below,

Applying triangle rule of vector addition in the triangle ABC, we get,

\overrightarrow{AC} =\overrightarrow{AB} +\overrightarrow{BC}..(1)

Similarly applying triangle rule of vector addition in triangles ADE and ACD we get,

\overrightarrow{DA} =\overrightarrow{DE} +\overrightarrow{EA}...(2)

\overrightarrow{AC} +\overrightarrow{CD} = \overrightarrow{AD}...(3)

Therefore,

\overrightarrow{AB} +\overrightarrow{BC} +\overrightarrow{CD} +\overrightarrow{DE} +\overrightarrow{EA}

Now, let us group the above expression, so that we can compare it with the above equations.

=(\overrightarrow{AB}+\overrightarrow{BC}) + \overrightarrow{CD} + (\overrightarrow{DE} +\overrightarrow{EA})

=\overrightarrow{AC} +\overrightarrow{CD} +\overrightarrow{DA}

Substituting equation (1)

=\overrightarrow{AD} +\overrightarrow{DA}

= \overrightarrow{AD} -\overrightarrow{AD}

= 0

Hence proved.

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Answered by DarshanBikashSaikia
31

Answer:

Answer is given above.

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