Answer to Question #25713 in Algebra for tyc

Question

Given a plane"s equation as 8x+15y-3z-17=0
Write the equation as (x-h) + b(y-k) + c (z-1) = 0 and hence write the normal to the plane and point that passes through the plane.

Answer 1

Condition of the problem: 8x+15y-3z-17=0

write the normal to the plane and point that passes through the plane

Solution: 8x+15y-3z-17=0

1) take the equation to the given form:

x + 15/8y - 3/8z - 17/8=0

(x-5/8) + 15/8(y-1) - 3/8(z-1)=0

2) we can see that plane equation is now in canonical form.

So normal coordinates are the coefficients beside the variables

normal n=(1 , 15/8 , -3/8)

and point coordinates are subtracted from variables

point (5/8 , 1 , 1)

we can easily check the answers by substitution