Question

Find the Cartesian equations of the line which passes through the point (–2, 4, –5) and parallel to the line `(x + 2)/(3) = (y - 3)/(5) = (z + 5)/(6)`.

Answer 1

The line `(x + 2)/(3) = (y - 3)/(5) = (z + 5)/(6)` has direction ratios 3, 5, 6.

The required line has direction ratios 3, 5, 6 as it is parallel to the given line.

It passes through the point (– 2, 4, – 5).

The cartesian equation of  the line passing through (x₁, y₁, z₁) and having direction ratios a, b, c are 

`(x- x_1)/a = (y- y_1)/b = (z - z_1)/c`

∴ The required cartesian equation of the line are

`(x - (-2))/(3) = (y - 4)/(5) = (z - (-5))/(6)`

i.e. `(x + 2)/(3) = (y - 4)/(5) = (z + 5)/(6)`.