- #1

mr_coffee

- 1,629

- 1

Hello everyone, I'm stuck on some problems, This is the first homeowrk assignment and i'm pretty lost! i'm going to list the directions and show you what I have done so far, any help would be great!

Here is my work to the problems:

//http://img175.imageshack.us/img175/4090/4108rz.jpg [Broken]

//http://img217.imageshack.us/img217/919/13192yq.jpg [Broken]

//http://img217.imageshack.us/img217/1842/22403rs.jpg [Broken]

#4. What are the projections of the point (2,3,5) on the xy-,yz-, and xz-planes? Draw a rectangular box with the origin and (2,3,5) as opposite verticies and with its face parallel to the coordinate planes. Label all vertices of the box. Find the length of the diagnoal of the box.

#7. Show that the triangle with vertices P(-2,4,0), Q(1,2-1), and R(-1,1,2) is an equialteral triangle. I used the distance formula from RP and to PQ, and they didn't equal eachother as shown in the drawing. SO doesn't that right there prove it isn't an equialteral triangle? or did i screw up?

#10. Find the distance from (3,7,-5) to each of the following.

(a) THe xy-plane

(b) The yz-plane

(c) The xz-plane

(d) the x-axis

(e) the y-axis

(f) the z-axis

I know this is probably easy but I'm not sure on how you would start this problem. Of course you would use the distance formula, but what would u choose for the 2nd point?

#19. Prove that the midpoint of the line segment from P1(x1,y1,z1) to P2(x2,y2,z2) is ([x1+x2]/2, [y1+y2]/2, [z1+z2]/2); (b) find the lengths of the medians of the triangle with vertices A(1,2,3),B(-2,0,5); C(4,1,5). The answer to B is: 5/2, 1/2 *sqrt(94), 1/2*sqrt(85);

#25. Describe in words the region of R^3 representee by the equation or inequality. x > 3; answer: A half-space consisting of all points in front of plane x= 3. What is a half space? and what would it look like?

#28. y = z; I said a plane parrallel to the xz-plane. I just treated z as being a constant like k. But i'm sure that isn't right. or is it?

#34. xyz = 0; I have no idea what this would be in words or visually.

#40. Consider the points P such that the distance from P to A(-1,5,3) is twice the distance from P to B(6,2,-2). Show that the set of all such points is a sphere, and find its center and radius. I'm fine on finding the center and radius of problems but i'm stuck on the first part, any hints?

Thanks!

Here is my work to the problems:

//http://img175.imageshack.us/img175/4090/4108rz.jpg [Broken]

//http://img217.imageshack.us/img217/919/13192yq.jpg [Broken]

//http://img217.imageshack.us/img217/1842/22403rs.jpg [Broken]

#4. What are the projections of the point (2,3,5) on the xy-,yz-, and xz-planes? Draw a rectangular box with the origin and (2,3,5) as opposite verticies and with its face parallel to the coordinate planes. Label all vertices of the box. Find the length of the diagnoal of the box.

#7. Show that the triangle with vertices P(-2,4,0), Q(1,2-1), and R(-1,1,2) is an equialteral triangle. I used the distance formula from RP and to PQ, and they didn't equal eachother as shown in the drawing. SO doesn't that right there prove it isn't an equialteral triangle? or did i screw up?

#10. Find the distance from (3,7,-5) to each of the following.

(a) THe xy-plane

(b) The yz-plane

(c) The xz-plane

(d) the x-axis

(e) the y-axis

(f) the z-axis

I know this is probably easy but I'm not sure on how you would start this problem. Of course you would use the distance formula, but what would u choose for the 2nd point?

#19. Prove that the midpoint of the line segment from P1(x1,y1,z1) to P2(x2,y2,z2) is ([x1+x2]/2, [y1+y2]/2, [z1+z2]/2); (b) find the lengths of the medians of the triangle with vertices A(1,2,3),B(-2,0,5); C(4,1,5). The answer to B is: 5/2, 1/2 *sqrt(94), 1/2*sqrt(85);

#25. Describe in words the region of R^3 representee by the equation or inequality. x > 3; answer: A half-space consisting of all points in front of plane x= 3. What is a half space? and what would it look like?

#28. y = z; I said a plane parrallel to the xz-plane. I just treated z as being a constant like k. But i'm sure that isn't right. or is it?

#34. xyz = 0; I have no idea what this would be in words or visually.

#40. Consider the points P such that the distance from P to A(-1,5,3) is twice the distance from P to B(6,2,-2). Show that the set of all such points is a sphere, and find its center and radius. I'm fine on finding the center and radius of problems but i'm stuck on the first part, any hints?

Thanks!

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