Q. 19

# Find the shortest

Given : Cartesian equations of lines  To Find : 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, Given Cartesian equations of lines Line L1 is passing through point (12, 1, 5) and has direction ratios (-9, 4, 2)

Therefore, vector equation of line L1 is And Line L2 is passing through point (23, 10, 23) and has direction ratios (-6, -4, 3)

Therefore, vector equation of line L2 is Now, to calculate distance between the lines,  Here,    Therefore,      = 65  Now,  = 220 + 135 + 1080

= 1435

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.
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 RELATED QUESTIONS :

Find the shortestMathematics - Board Papers

Show that the linMathematics - Board Papers

Find the shortestMathematics - Board Papers

Find the shortestMathematics - Board Papers