Q. 15

Find the vector equation of a line passing through the point (2, 3, 2) and parallel to the line Also, find the distance between these lines.

HINT: The given line is



The required line is



Now, find the distance between the parallel lines L1 and L2.

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






Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Revision of straight lines important formulas in one shot59 mins
Concept Builder Questions of straight Lines (Quiz Session)55 mins
Magnetic field due to current carrying straight wire37 mins
Translation Process37 mins
Interactive Quiz on Bacterial Diseases29 mins
Immune System Disorders60 mins
Interactive Quiz on Cancer36 mins
Interactive Quiz on Magnetic field due to straight wire & circular loop41 mins
Interactive Quiz on Connective & Epithelial Tissue45 mins
Human health & diseases (Drug)56 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses