Answer to Question #7395 in Analytic Geometry for paaven reddy

Question

the line 2y+7x=5 and 4x+dy+3=0 are perpendicular to each other, find the value for d.

Answer 1

First, we need to have both lines equations in the form ax+by+c=0. So, we obtain
7x+2y-5=0
4x+dy+3=0
If two lines are perpendicular then their normal vectors are perpendicular as well. For lines written in the above form finding of normal vector is pretty easy - its coordinates are& umbers beside x and y in the equation. So, for the first line we have {7,2}, fo the second {4,d}
If two vectors are perpendicular then their dot product equals zero.& Therefore
7*4+2*d=0
whence d=-28/2=-14