#### Question

Find the Cartesian equation of the line which passes through the point (−2, 4, −5) and parallel to the line given by `(x+3)/3 = (y-4)/5 = ("z"+8)/6`

#### Solution

It is given that the line passes through the point (−2, 4, −5) and is parallel to

`(x+3)/3 = (y-4)/5 = (z+8)/6`

The direction ratios of the line,

`(x+3)/3 = (y-4)/5 = (z+8)/6` are 3, 5, and 6.

The required line is parallel to `(x+3)/3 = (y-4)/5 = (z+8)/6`

Therefore, its direction ratios are 3*k*, 5*k*, and 6*k*, where *k* ≠ 0

It is known that the equation of the line through the point (*x*_{1}, *y*_{1}, *z*_{1}) and with direction ratios, *a*, *b*, *c*, is given by `(x-x_1)/a = (y-y_1)/b = (z-z_1)/c`

Therefore the equation of the required line is

Is there an error in this question or solution?

Solution Find the Cartesian Equation of the Line Which Passes Through the Point (−2, 4, −5) and Parallel to the Line Given by `(X+3)/3 = (Y-4)/5 = (Z+8)/6` Concept: Equation of a Line in Space.