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

the cartesian equation of the line can be written as

We have written the above equation ion this way because the coefficients of x, y, z must be 1

Therefore the direction ratios of the above line are ‹a, 1, c›

Let

Therefore x = b + a, y = , z = d + c….(1)

….(2)

Hence comparing 1&2

The vector equation of the line is given as