How to find shortest distance between two lines

SHORTEST DISTANCE BETWEEN TWO LINES

1st of all we shall find out shortest distance between two Parallel lines.

Problem 1

Consider two parallel lines whose equations in vector form are given by

 Now comparing these equations with standard form , and write

 _, and  vectors ,we get

Now applying this formula to find the shortest distance between two lines .

As it is clear from formula , we have to find cross product of  and  and then magnitude of vector 

Now find the magnitude of  × vector

                                 =√(81)+(196)+(16)

                                 =√293

Magnitude of 

                    = √49

           = 7

Putting all these values in  the formula of Shortest Distance between two lines .

Now Find distance between two skew lines i.e. Lines which are not Parallel lines.

Problem 2

Consider two parallel lines whose equations in vector form are given by

 Now comparing these equations with standard form , and write

 _, and  vectors ,we get

 Now applying this formula to find the shortest distance between two lines 

 Now find cross product and then  magnitude of these two vectors

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FINAL WORDS

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