Maharashtra State BoardHSC Arts 12th Board Exam
Advertisement Remove all ads

If the Lines (x-1)/2=(y+1)/3=(z-1)/4  and (x-3)/1=(y-k)/2=z/1  Intersect Each Other Then Find Value of K - Mathematics and Statistics

Sum

If the lines `(x-1)/2=(y+1)/3=(z-1)/4 ` and `(x-3)/1=(y-k)/2=z/1` intersect each other then find value of k

Advertisement Remove all ads

Solution

Let `(x-1)/2=(y+1)/3=(z-1)/4 =u ` where is any constant.

So for any point on this line has co-ordinates in the form (2u+1,3u-1,4u+1)

`(x-3)/1=(y-k)/2=z/1=v`

So for any point on this line has co-ordinates in the form   (v+3,2v+k,v).

Point of intersection of these two lines will have co-ordinates of the form

(2u +1, 3u −1,4u +1) and (v +3, 2v + k,v) .

Equating the x, y and z co-ordinates for both the forms we get three equations

 2u+1=v+3

2u-v=2.............(1)

3u-1=2v+k

3u-2v=k+1.......(2)

4u+1=v

4u-v=-1...........(3)

Subtracting equation (1)from equation(3) we get,

2u = -3

u=-3/2

Substitute value of u in equation (1) we get,

2(-3/2) - v=2

v=-5

Substitute value of v and in equation (2) we get,

3(-3/2) - 2(-5)=k+1

k=9/2

the value of k is 9/2

Concept: Concept of Line - Distance of a Point from a Line
  Is there an error in this question or solution?
Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×