The cartesian equations of a line are x = ay + b, z = cy + d. Find its direction ratios and reduce it to vector form.

Question

jamesj · Answer

By way of example, consider the line
y = 2x + 3

then for every +1 of x, y changes by +2

Hence in vector form, the line is

(1,2)t + (0,3)

jamesj · Answer

Apply this idea to your problems.

vishweshshrimali5 · Answer

sorry sir that is not working.

Will you please explain me how to solve it

jamesj · Answer

Ok, so what is the vector form of the line y = x ?

vishweshshrimali5 · Answer

$$y = x => y - x = 0 => j - i = 0 => i = j$$ I hope I am right

jamesj · Answer

Well, not quite, because i is not j.  But what is true is that for any t, the vector
t i + t j
is on the line.

jamesj · Answer

This is expression is what I mean by the vector form of the line.  We can also write it as 
v = t(1,1)
or 
v = t (i + j)