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ABCDEF is a hexagon, where \overrightarrow{AB}=\hat{i}-\hat{j},\: \: \: \overrightarrow{BC}=\hat{i}+\hat{j},\: \: \: \overrightarrow{CD}=-2\hat{i}+\hat{j},\overrightarrow{DE}=-\hat{i},\: \: \: \overrightarrow{EF}=\hat{j}-\hat{i} then vector \overrightarrow{FA} equals

Option: 1

2\hat{i}-2\hat{j}


Option: 2

2\hat{i}+2\hat{j}


Option: 3

-2\hat{i}+2\hat{j}


Option: 4

-2\hat{i}-2\hat{j}


Answers (1)

best_answer

As we learned

Polygon Law -

Polygon law of vector addition states that if a number of vectors are represented by side of polygon taken in order, their resultant is fully represented by the closing side of polygon taken opposite order.

- wherein

Fig 3

 

 Resultant of all vectors will be \overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{CD}+\overrightarrow{DE}+\overrightarrow{EF} ans will be along \overrightarrow{AF}

\overrightarrow{AF}=-2\hat{i}+2\hat{j}\Rightarrow \overrightarrow{FA}=2\hat{i}-2\hat{j}

\therefore option(A)

 

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rishi.raj

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