Question

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 k​

Answer 1

Step-by-step explanation:

the first line is given by

x-1/2=y+1/3=z-1/4=l

therefore

x-1=2l

x=2l+1

y+1=3l

y=3l-1

z-1=4l

z=4l+1

this is the first line coordinates(2l+1,3l-1,4l+1)

the secound line is given by

x-3/1=y-k/2=z/1=m

therefore

x-3=m

x=m+3

y-k=2m

y=2m+k

z=m

this is the secound line coordinates(m+3,2m+k,m)

if the two lines intersect each other

2l+1=m+3

2l-m=2

4l+1=m

4l-m=-1

by substituting these two equations

l=-3/2 andm=-5

3l-1=2m+k

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

-9/2-1=-10+k

-11/2+10=k

k=9/2

the k value is 9/2