Answer :

We are given with two lines.

…(i)


…(ii)


Take equation (i),





…(iii)


We know that,


Vector equation of a line passing through a point and parallel to a vector is , where λ .




Comparing it with equation (iii), we get




Now, take equation (ii),



…(iv)


Similarly from (iv),




So,


Shortest distance between two lines is given by



Solve .



Take 1st row and 1st column, multiply the first element of the row (a11) with the difference of multiplication of opposite elements (a22 × a33 – a23 × a32), excluding 1st row and 1st column.



Here,



Now take 1st row and 2nd column, multiply the second element of the row (a12) with the difference of multiplication of opposite elements (a21 × a33 – a23 × a31), excluding 1st row and 2nd column.



Here,



Similarly, take 1st row and 3rd column, multiply the third element of the row (a13) with the difference of multiplication of opposite elements (a22 × a33 – a23 × a32), excluding 1st row and 3rd column.



Here,



Further, simplifying it.




…(v)


And,








…(vi)


Now, solving .




…(vii)


Substituting values from (v), (vi) and (vii) in d, we get







d = 14


Thus, the shortest distance between the given lines is 14 units.


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