Question

Show that the lines x-1/3=y-1/-1=z+1/0 and x-4/2=y/0=z+1/3 intersect. Find their point of intersection.

Answer 1

Let the above two lines intersect at point P

(x-1)/2=(y+2)/3=(z-1)/4=r(let)…………(1)

coordinate of P which lies on the above lines is

(2r+1,3r-2,4r+1)

P also lies on eq.(2)

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

(2r+1–3)/1=(3r-2-k)/2=(4r+1)/1

2r-2=(3r-2-k)/2=4r+1

2r-2=4r+1

-2r=3 => r =-3/2

(3r-2-k)/2=4r+1

(-9/2–2-k)/2=4×(-3/2)+1

(-13/2-k)/2=-5

-13/2-k=-10

10–13/2=k

7/2=k

k=7/2=3.5 , Answer.