Q. 17

Write the vector equation of the following lines and hence find the shortest distance between them :

and

Answer :

Given : Cartesian equations of lines




To Find : i) vector equations of given lines


ii) distance d


Formulae :


1. Equation of line :


Equation of line passing through point A (a1, a2, a3) and having direction ratios (b1, b2, b3) is



Where,


And


2. Cross Product :


If are two vectors




then,



3. Dot Product :


If are two vectors




then,



4. Shortest distance between two lines :


The shortest distance between the skew lines and


is given by,



Answer :


Given Cartesian equations of lines



Line L1 is passing through point (1, 2, 3) and has direction ratios (2, 3, 4)


Therefore, vector equation of line L1 is



And



Line L2 is passing through point (2, 3, 5) and has direction ratios (3, 4, 5)


Therefore, vector equation of line L2 is



Now, to calculate distance between the lines,




Here,






Therefore,










Now,




= - 2 + 2 - 2


= -2


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
Human health & diseases (Drug)56 mins
Get to know all about Immune System60 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