# math

posted by .

Given the plane 2x-3y+7z=4,

a) Find the equation for the line perpendicular to the plane that intersects the plane at the point P=(6,5,1).
b) How far is it from the point (4,-2,3) to the plane?

• math -

a)(x-6)/2=(y-5)/(-3)=(z-1)/7
b)The normal equation of the plane
(2/sqrt(62))x-(3/sqrt(62))y+(7/sqrt(62))z-
-4/sqrt(62)=0 62=2^2+(-3)^2+7^2

The distance=(2*4-3*(-2)+7*3-4)/sqrt(62)=
sqrt(31/2)

• math -

why do you have = signs in part a?

## Similar Questions

1. ### Geometry

a line RS is perpendicular to plane p at R. If T is a second point not on. Can RT be perpendicular to plane P?
2. ### Math

a line RS is perpendicular to plane p at R. If T is a second point not on. Can RT be perpendicular to plane P?
3. ### Math

Given the plane 2x-3y+7z=4, find the equation for the line perpendicular to the plane that intersects the plane at the point (6,5,1).
4. ### Math

Okay heres the pic. There is a plane with points B,D, and E.those [oints are collinear in the plane. And also outside of the plane is points A, and C. and those points are collinear outside of the plane.thought Line AC intersect at …
5. ### Precalc

At the point were a line intersects a plane [with the equation (24x+32y+40z=480) and three points of A(5, 10, 1), B(6, 3, 6), and C(12, 1, 4)], the vector i-, vector j-, and vector k-coefficients of the line equal the corresponding …
6. ### Geometry

4.Determine which point does not lie on the graph of the line y=x-3 a. (-10, 13) b. (-10-13) c. (-8, -11) A?
7. ### Calculus

Find the scalar equation of a plane that is perpendicular to plane r=(-2,1,3)+s(0,1,1)+t(-1,0,3) and also intersects it along the line (x-3)/2=(y+1)/-3,z=1
8. ### Geometry

Plane R contains points ,M,and Y. Plane Z intersects with plane R at SM, AY intersects plane R at point Y. . Point A is not in plane Z or plane R. MY forms a right angle with MS. A. What is measure of < SMY?
9. ### Calculus

a) Find parametric equations for the line through (4, 1, 4) that is perpendicular to the plane x − y + 2z = 7. (Use the parameter t.) b) In what points does this line intersect the coordinate planes?
10. ### math

Hi, I was working on my math homework and I was stumbling on these problems. I tried looking at the solutions but my answers were completely off. Here are the ones I'm stuck on: If vectors O(0,0,0), A(6,0,0), B(6,-sqrt(24), sqrt(12)), …

More Similar Questions