Question

Show that the line joining the point (4,7,8), (2,3,4), is parallel to the line joining the point (2,4,10) (-2,-4,2).

Answer 1

line joining the point (4,7,8), (2,3,4), is parallel to the line joining the point (2,4,10) (-2,-4,2).direction ratios  of line 1

we know for parallel lines ratio of a1/a2=b1/b2=c1/c2 should be same

line 1 points  (4,7,8), (2,3,4),

a1=x2-x1=2-4=-2

b1=     y2-y1.=3-7=-4

c1=   z2,-z1=4-8=-4

line 2 points (2,4,10) (-2,-4,2)

a2=x2-x1=-2-2=-4

b2=y2-y1=-4-4=-8

c2=z2-z1=2-10=-8

a1/a2=b1/b2=c1/c2

(-2/-4)=-4/-8=-4/-8

1/2=1/2=1/2

hence lines are parallel