Question

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

Answer 1

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)

Answer 2

Apply this idea to your problems.

Answer 3

sorry sir that is not working.

Will you please explain me how to solve it

Answer 4

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

Answer 5

\[y = x => y - x = 0 => j - i = 0 => i = j\] I hope I am right

Answer 6

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.

Answer 7

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)