# Calculus

I'm having trouble with this one.

Problem: Find the equations for the planes parallel to x+2y-2z=1 and two units away from it.

1. 👍
2. 👎
3. 👁
1. If a point (p,q,r) is not on the place Ax+By+Cz+D = 0 then the distance to the plane is

(Ap + Bq + Cr + D)/(sqrt(A^2+B^2+C^2))

So let the new equation be x + 2y - 2z + D = 0
and pick any point which satisfies the given equation, say (1,0,0)

So the distance is (1 + 4 + 4 + C)/sqrt(1+0+0)
= (1+D)/sqrt(5) but this is supposed to be 2

(1+D)/sqrt(5) = 2
D = 2SQRT(5) - 1

x + 2y - 2z + 2SQRT(5) - 1 = 0

1. 👍
2. 👎
2. I put the 4's in the wrong place, it should have said

"So the distance is (1 + 0 + 0 + C)/sqrt(1+4+4)
= (1+D)/sqrt(5) but this is supposed to be 2 "

the rest of the post is ok

1. 👍
2. 👎

## Similar Questions

1. ### Calculus

A curve is defined by the parametric equations: x = t2 – t and y = t3 – 3t Find the coordinates of the point(s) on the curve for which the normal to the curve is parallel to the y-axis. You must use calculus and clearly show

2. ### math help

find a set of parametric equations for the line through the point and parallel to the specified vector. (1, -8, -3), parallel to (-1, 6, -6) find symmetric equations for the line through the point and parallel to the specified

3. ### Calculus

Consider the following planes. 5x − 4y + z = 1, 4x + y − 5z = 5 a) Find parametric equations for the line of intersection of the planes. b) Find the angle between the planes

4. ### math

An airline with two types of airplanes, P1 and P2, has contracted with a tour group to provide transportation for a minimum of 400 first class, 900 tourist class, and 1500 economy class passengers. For a certain trip, airplane P1

1. ### Analytic Geometry

Given two planes, discuss the methods used to determine if the planes are parallel, perpendicular, coincident, or none of these.

2. ### Math

1. Determine the scalar equation of the plane with vector equation Vector r= (3,-1,4) +s(2,-1,5) + t(-3,2,-2). 2. Determine the value of k so that the line with parametric equations x = 2 + 3t, y = -2 + 5t, z = kt is parallel to

3. ### Calculus

Find the distance between the given parallel planes. 5x−4y+z=10, 10x−8y+2z=3

4. ### algebra

Two planes left simultaneously from the same airport and headed in the same direction towards another airport 1800 km away. The speed of one of the planes was 100 km/hour slower than the speed of the other plane, and so it arrived

1. ### Calculus

Consider the planes given by the equations 2y−2x−z=2 x−2y+3z=7 (a) Find a vector v parallel to the line of intersection of the planes. (b)Find the equation of a plane through the origin which is perpendicular to the line of

2. ### Calculus

Determine the intersection, if any, of the planes with equations x + y - z + 12 = 0 and 2x + 4y - 3z + 8 = 0. I have no clue where to even begin. If someone could help and give me the steps to complete it, that would be greatly

3. ### Calc.

I am so confused with this last part of the unit! What in the world is going on: Use normal vectors to determine the interaction, if any, for each of the following pairs of planes. Give a geometric interpretation in each case and

4. ### Math

Two planes left simultaneously from the same airport and headed in the same direction towards another airport 3600 km away. The speed of one of the planes was 200 km/hour slower than the speed of the other plane, and so it arrived