Question

Show that the lines (x-1)/3=(y-1)/-1 , z+1=0 and ( x-4)/2=(z+1)/3 , y=0 intersect each other . Also find their point of intersection.
thank you

Answer 1

Solution :

x−13=y−1−1x−13=y−1−1,z+1=0,z+1=0----------(1)

Let x−13=y−1−1x−13=y−1−1=k=k

x=3k+1,y=−k+1x=3k+1,y=−k+1 and z=−1z=−1

x−42=z+13x−42=z+13y=0y=0----------(2)

Let x−42=z+13x−42=z+13=m=m

x=2m+4,z=3m−1,y=0x=2m+4,z=3m−1,y=0

If they intersect , they should have a common point.

y=−k+1y=−k+1 and y=0y=0 and 2=3m−12=3m−1 and z=−1z=−1

−k+1−k+1 and m=0m=0

Hence x=3(1)+1,y=−1+1,z=−1x=3(1)+1,y=−1+1,z=−1

(i.e) x=4,y=0,z=−1x=4,y=0,z=−1

Hence substituting for m=0=>x=4m=0=>x=4.

Hence the lines intersect.

and the points of intersection is (4,0,−1)

Answer 2

Answer:

i didn't know what is going to happen