How to find shortest distance between two lines ~ Simplifying Reasoning problem, Ssc cgl Reasoning tricks , logical reasoning questions with answers

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

HOW TO FIND SHORTEST DISTANCE BETWEEN TWO LINES

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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