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  • 7 straight lines are there in a plane, such that no two are parallel and no three are concurrent, then number of parts in which the plane will be divided by these lines is <div class=

7 straight lines are there in a plane, such that no two are parallel and no three are concurrent, then number of parts in which the plane will be divided by these lines is 

Option: 1

27 


Option: 2

29 


Option: 3

31 


Option: 4

33 


Answers (1)

best_answer

Observe that if we have only one line, then it divides the plane in 2 parts

Then if we add a second line ( which is non parallel) , then total number of parts of the plane becomes 4  (increases by 2)

Then if we add third line, then total number of parts of plane becomes 7  (increases by 3)

Similarly for fourth line, the number of parts increases by 4, and so on

So, number of parts = 2 + (2+3+.....+7 ) = 1 + ( 1+2+3+......+7)

                              = 1+ \frac{7 \times 8 }{2 } = 29

Posted by

Ritika Harsh

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