No links please Q (ii) The Cartesian equations of a line are x = ay + b, z = cy - Maths - Inverse Trigonometric Functions

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Q (ii) The Cartesian equations of a line are x = ay + b, z = cy + d
Find its direction ratios
2 d (ii) Ans : < a, 0, c >

Rishabh Mittal · Accepted Answer

Given cartesian equations of a line

$x = a y + b, z = c y + d$

We need to find the direction ratios of the line.

Consider the equation:

$x = a y + b x - b = a y \frac{x - b}{a} = y$

That is,

$y = \frac{x - b}{a}$ ......(1)

Now consider the next equation:

$z = c y + d$

$z = c y + d z - d = c y \frac{z - d}{c} = y$

That is,

$y = \frac{z - d}{c}$ ......(2)

Compare both the equations (1) and (2) to get

$\frac{x - b}{a} = \frac{y}{1} = \frac{z - d}{c}$ .......(3)

Thus, the direction ratios of the line are $a, 1 a n d c$

No links please Q.(ii) The Cartesian equations of a line are x = ay + b, z = cy + d. Find its direction ratios. 2.d (ii) Ans : < a, 0, c >