Question

the two lines x=ay+b, z= cy+d and x=a'y+b', z=c'y+d' are perpendicular to each other, if:

(a) aa'+cc'=1
(b) (a/a') + (c/c') =-1
(c) (a/a')+(c/c')=1
(d) aa'+cc'=-1

Answer 1

the answer would be d
since we can rewrite the first two lines as
y=(x-b)/a y=(z-d)/c therefore ((x-b)/a)= ((z-d)/c)
which gives us <x,1,c>
similar we write the second two lines is that for giving us <x',1,z'>
and we know if they are perpendicular the dot product gives us 0
thus xx'+1+zz'=0

Answer 2

ok how did you get <x,1,c>??

Answer 3

i mixed up my signs halfway through it should be <a,1,c> and <a',1,c'>
and aa'+1+cc'=0

Answer 4

ohk that works.. thanx bro!