Q. 185.0( 1 Vote )

# Show that the lines and intersect. Find their point of intersection.

Given: and Now, let x – 1 = 3λ, y – 1 = -λ and z + 1 = 0

x = 3λ + 1, y = -λ + 1 and z = -1

Let x – 4 = 2μ, y = 0 and z + 1 = 3μ

x = 2μ + 4, y = 0 and z = 3μ – 1

If lines intersect, then they have a common point for some value of λ and μ

So, 3λ + 1 = 2μ + 4 [comparing the values of x]

3λ – 2μ = 4 – 1

3λ – 2μ = 3 …(i)

and –λ + 1 = 0 [comparing the values of y]

λ = 1

and -1 = 3μ – 1

-1 + 1 = 3μ

μ = 0

Now, putting the values of λ and μ in eq. (i), we get

3(1) – 2(0) = 3

3 = 3

Since, λ = 1 and μ = 0 satisfy equation (i) so the given lines intersect.

Now, the point of intersection are

x = 3λ + 1, y = -λ + 1 and z = -1

x = 3(1) + 1, y = -(1) + 1 and z = -1

x = 4 , y = 0 and z = -1

Point of intersection are (4, 0, -1)

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Know all about Infertility39 mins  Clear all concepts about AIDS46 mins  All About Faraday's law55 mins  Get to know all about Immune System60 mins  Revision Class | All Formulas of Electrodynamics63 mins  Biotech Application- All Concepts at Fingertips73 mins  All Important Questions on Bio Molecules46 mins  Know all about Colligative Properties50 mins  Know All About Types of Relations53 mins  All concepts of Hybridisation in 60 minutes41 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 