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+8/6 - Maths - Three Dimensional Geometry

Question

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+8/6

Varun.Rawat · Accepted Answer

The equation of the given line is,   x+33 = 4-y5 = z+86⇒x+33 = y-4-5 = z+86       
1The direction ratios of line 1 are : 3,-5,6Now, direction ratios of required line that is parallel to line 1 will be 3,-5,6
We know that cartesian equation of a line passing through x1,y1,z1 and having direction ratios a,b,c is given byx-x1a = y-y1b = z-z1cNow, the equation of the required line that passes through -2,4,-5 and having direction ratios 3,-5,6 isx+23 = y-4-5 = z+56