# Show that the lin

Given equations :  To Find : d

Formula :

1. Cross Product :

If are two vectors  then, 2. Dot Product :

If are two vectors  then, 3. Shortest distance between two lines :

The shortest distance between the skew lines and is given by, For given lines,  Here,    Therefore,        Now,  = - 15 – 18 + 33

= 0

Therefore, the shortest distance between the given lines is   As d = 0

Hence, the given lines not intersect each other.

Now, to find point of intersection, let us convert given vector equations into Cartesian equations.

For that substituting in given equations,      General point on L1 is

x1 = 2λ+1 , y1 = 3λ+2 , z1 = 4λ+3

let, P(x1, y1, z1) be point of intersection of two given lines.

Therefore, point P satisfies equation of line L2.  4λ – 6 = 15λ + 5

11λ = -11

λ = -1

Therefore, x1 = 2(-1)+1 , y1 = 3(-1)+2 , z1 = 4(-1)+3

x1 = -1 , y1 = -1 , z1 = -1

Hence point of intersection of given lines is (-1, -1, -1).

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