# If lines <s

Given the equation of line are-

any random point on this line is given by (2λ+1, 3λ-1, 4λ+1)

Another line is:

any random point on this line is given by (μ+3, 2μ+k, μ)

At point of intersection of the lines the random coordinates must coincide.

2λ + 1 = μ+3

2λ - μ = 2 …(1)

Also,

4λ + 1 = μ

μ = 4λ + 1 …(2)

Adding equation 1 and 2,we get-

2λ = 4λ + 3

As, 3λ – 1 = 2μ + k

we have the values of λ and μ.

k = 3λ – 2μ – 1

k = 3(-3/2) – 2(-5) – 1

k = 9/2

Now we need to find the equation of the plane containing these 2 lines.

For this we need the normal vector to plain and a point on plane.

For normal we need to take the cross product of direction ratios of line.

Direction ratio of line 1 is (2,3,4)

And direction ratio of line 2 is ( 1,2,1)

the normal vector is given as -

Let be any random vector on pthe lane.

The equation of plane is given by –

where a is any defined vector on planthe e.

As lines lie on a plane, so one of its points can be taken as a poi t on the plane.

(2λ+1, 3λ-1, 4λ+1) will give a point on putting λ = 0

Point is (1, -1, 1)

Hence, the equation of the plane is:

-5x + 2y + z = -5-2+1 = -6

Equation is: -5x+2y+z = -6

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 equationMathematics - Board Papers

Show that the linMathematics - Board Papers

If lines <sMathematics - Board Papers

Let <span lang="EMathematics - Board Papers

Prove that the liRS Aggarwal - Mathematics

Prove that the liRS Aggarwal - Mathematics

Find the equationRS Aggarwal - Mathematics