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

Explanation

As these two lines are parallel, their direction ratios will be in equal ratios.

Equation of the given line is,

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

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

So,direction ratios of the given line is `(3,-5,6)`.

As the line is passing through `(-2,4,-5)` so, equation of the required line will be,

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

`=>(x+2)/3 = (4-y)/5 = (z+5)/6`, which is the required equation.