# planes

1. ### Solution to intersecting planes

Regarding the image below, I'm confused where the variable r came from. Can someone please explain?
2. ### Equations of a line through a point, intersects z axis, and parallel to a plane

A question on my review guide asks for me to find the parametric equations of the line through the point (3,6,4) that intersects the z-axis and is parallel to the plane x − 3y + 5z = 6 . The answer should be (x = 3t + 3, y = 6t + 6 z = 3t + 4) Any help is appreciated!
3. ### volume bounded by planes y = (x^2) , planes z = 0 , , z = 4 and y = 9

by using triple integral , find the volume bounded by planes y = (x^2) , planes z = 0 , , z = 4 and y = 9 . My ans is 36 , but the ans is 144... Is my ans wrong ?
4. ### formula for the angle between two intersectiing planes

Hello, Referring to the picture below, I have 4 points in orthogonal 3D space (sorry if I couldn't make the picture look more 3d). The vectors AB and BC lie in an Euclidian plane while the vectors AB and BD lie in a different Euclidian plane. These planes intersect along the vector AB. I am...
5. ### Intersection between 2 Planes

I need to find the vector equation that describes the intersection between the plane 121x+115y+12 674 660z=-890383 and the plane z=0. I understand how to find intersections of 2 planes using matrix row reduction, but the z=0 part threw me off. Any help would be greatly appreciated. Thanks I
6. ### Help with intersecting planes and a line

Hi, I'm having trouble figuring out this problem: Two planes intersect in line A, which then crosses another line B. Find the coordinate for the intersection between lines A and B. Planes: x+y+3z+6=0 2x+y-2z-10=0 Coordinates for line B: (6,0,1) and (-4,4,7) I tried solving it like this, step...
7. ### line of intersection between two parallel planes

How can I find the line of intersection between the planes 2x-y+2x+1=0 and -4x+2y-4x-2=0 I realize these are parallel as they are multiples of each other, but I'm not sure how to solve for the point. I also have to convert this line into parametric, cartesian and vector form. Sorry for the...
8. ### Find the equation of the plane given a point and two planes

I've done a question similar to this, however this one has no complete equations i can solve for. Determine the equation of the plane that passes through (1,3,8)(1,3,8) and is perpendicular to the line of intersection of the planes 3x−2z+1=03x−2z+1=0 and 4x+3y+7=04x+3y+7=0. I know to take the...
9. ### planes , calculus help

Determine whether the two lines and are parallel, skew, or intersecting. If they intersect, find the point of intersection.Match two lists. and and and and and and A Intersect at the point (2−13) B and are parallel lines. C and are skew lines. D...
10. ### vectors and planes!

Plane flying downward toward a runway at 154mph makes an angle of 6 degrees with runway.v = ? I must have the answer in __ i +/- __ j
11. ### Vectors - lines and planes (again)

Wow, these questions are really beginning to bother me, everything else in my syllabus and past papers are a breeze until i get to a vectors question... Anyway, my question is: Find a vector equation of the line through (4,2, -3), parallel to the line of intersection of the planes 3x - 2y =6...
12. ### Vectors - Planes

Hey all, can anybody do a step by step to this vector question? question is: "Find the perpendicular distance of the point (p,q,r) from the plane ax + by + cz =d I can do it if it has actual numbers but this makes it more difficult. cheers :)
13. ### Pure Maths: Vectors and Planes Problems

Hi, I'm really having trouble with questions 12,13 and 14. I think it involves using normals, perpendiculars and etc. Can somebody please take me through these questions? ANS: 12: r=-7i+3j + t(33i-9j+k) 13: r=4i+2j-3k + t(2i, 3j, -4k) 14: 2x+y-z+0
14. ### The geometrical relationship between three planes

I have a problem with a question about planes. I have the following system of equations: x + 2y - 3z = 3 3x + y + 2z = 4 5x +7z = 5 The question is: Describe the geometrical relationship of the three planes represented by this system of equations. Could someone please tell me how to tackle...
15. ### Planes and Vector help

How do I do this? A plane containing the vectors A(3,2,1) and B(1,2,2) and the point (1,1,4) Calculate the unit normal, n, to the plane. Calculate the perpendicular distance from the origin to the plane. Thank you!
16. ### orthogonal planes

I have to find equation to the plane that contains line (-1,1,2) +(3,2,4)t and is perpendicular to plane 2x+y-3x+4=0
17. ### Points equidistant from planes

Find all points that are equidistant from 6x-12y+15z-9=0 and 12x+9y-20z-19=0. Thanks.
18. ### intersection between planes and planes

i cant the way of finding the intersection point. but i can understand the way of finding of intersection of normal . can someone show me other simpler way of finding the intersection point?
19. ### Decomposing vectors.

Take n = 2i + j - k as a normal vector of the plane p. Decompose the vector QO into the sum of two vectors; one of them is parallel to n and the other one is orthogonal to n. So far I got, Q(0,0,-1) and (0,0,0) for the origin. and QO = (0,0,1). n=2i+j-k o=ai+bj+ck (2+a)i+(1+b)j+(-1+c)k=0i+0j+k I...
20. ### Help with algebra (lines in space)

Given cartesian coordinates x=(z-1)/2, y=1. And p defined as 2x+y-z=1. 1. The plane p divides R3 into two parts. Find the unit vector perpendicular to p and pointing into the part containing the origin O. 2. Let P(x,y,z) be the point on the line l given by x=(z-1)/2 and y=1. Letting x=t for...