Answer :

Given : point A ≡ (2, 3, 2)


Equation of line :


To Find : i) equation of line


ii) distance d


Formulae :


1. Equation of line :


Equation of line passing through point A (a1, a2, a3) and parallel to vector is given by



Where,


2. Cross Product :


If are two vectors




then,



3. Dot Product :


If are two vectors




then,



4. Shortest distance between two parallel lines :


The shortest distance between the parallel lines and


is given by,



Answer :


As the required line is parallel to the line



Therefore, the vector parallel to the required line is



Given point A ≡ (2, 3, 2)



Therefore, equation of line passing through A and parallel to is




Now, to calculate distance between above line and given line,




Here,








= 7










Therefore, the shortest distance between the given lines is






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