8. Find the angles between the planes r + y = 1, 2x + y – 2z = 2

Q: The distance from the point P(2, 1, 0) to the plane 2x + y + 2z + 6 = 0 is 3.7 False True O O

A: We can answer the question in the following steps using the required formula.

Q: The angle between two planes is the smallest angle 0 between the planes 6x + 2y – 4z = 0 and - 7x +…

A: We will solve the problem

Q: The distance from (9,-6, 7) to yZ-plane is A9 O B. 6 OC. 166 OD. 85 O E.7

A: Distance of a point (a,b,c) from yz plane is as In yz plane x coordinate is zero and y= b and z= c.…

Q: Determine the angle between the following two planes: 4x - 3y2z - 2 = 0 3x + 2y + 5z-5=0

A:

Q: 3.4 Compute the angle between -- ). --- 1 y = 2 using a. (x, y) := x'y TBy, 2 В:- 1 b. (x, y) := x 3

A:

Q: Find the intersection of the plane: x - z = 6, and the line r(t) = (1,0, -,1) + t(4,9,2)

A:

Q: 4z: Given two lines (z++l, 5t-5,lot )f ( 34, zt+3, zt+1) located in Sicde plane, fine th plane ?

A: Equation of the plane passing through to lines can be calculated as below,

Q: If 0 is the acute angle between the planes x + y = 2 and x + y +2z = 6, then 2cos (e) = O 1 O 1 O 2…

A: Given equation of planes are x+y-2=0 and x+y+2z-6=0 Let Let A1 x + B1 y + C1z + D1 = 0 and A2x + B2y…

Q: 2. Find the distance between the given parallel planes. 2x +y+ 2z = 8 and 4x +2y + 4z +5 = 0

A: # we are entitled to solve one question at a time, please resubmit the other questions if you wish…

Q: What is the image of the vertical strip  {zϵC:−1<Re(z)<1} under e^z

A: A  conformal map is a one-one and onto analytic map. So, Re(z)=1 to a point. Here f1 is defined by,…

Q: 4. (a) Show that the line l given by l: 1= 2+3t, y=1+4t, z= 5+ 2t, te R, lies in the plane II given…

A: Given problem:- Show that the line  given by   l : x = 2 + 3t , y = 1 + 4t , z=5+2t ,t in R   lies…

Q: Evaluate ſſ, Vy² – x² dA where boundary of R is the parallelogram bounded by the four lines

A: In this question, we evaluate the double integral by using the change of variable. The region is…

Q: Show that the distance between the parallel planes                                          ax + by…

A:

Q: Use Green's Theorem to evaluate (V1+r) dr+2ry dy, where C is the triangle with vertices (0, 0),…

A:

Q: Find the acute angle (in degrees) between the planes Sz + 3y +5z 1 and 2z

A: P1 denotes plane 1 P2 denotes plane 2

Q: For planes 2x + y – z = 2 and 2x + 3y + 5z = 4,

A:

Q: 2. Given: WX = YZ; ZWXZ = ZYZX Prove: WXYZ is a parallelogram

A: Parallelogram

Q: 12. The line of intersection of the planes x + 2y + 3z = 1 and x – y + z = 1 |

A: Given: The line of intersection of the plane x+2y+3y=1 and x-y+z=1

Q: Match the surfaces (a)-(e) with the contour diagrams (1)-(V, (M)

A:

Q: The distance from (4,-5, 10) to yZ-plane is O A.4 O B. 5 C. /141 OD.10 OE. 125

A: Solution is given below:

Q: Q: To find an angle between planes 2x + 4y - 4z- 6 = 0 and 4x + 3 y+9=0.

A: We have to find the angle between the given two planes.

Q: show that the points AC!,l,4) B(2,2,2), coplanear (in the c(o,l,5) and D (1,0,5) are Same plane).

A:

Q: What angle does the line of interaction of the planes 2x+y-z = 0 and x+y+2z= 0 make with the…

A: The direction vector of the line of the interaction of the two planes is equal to the cross product…

Q: 24. The plane that contains the line x = 1 + t, y = 2 – t, z = 4 – 3t and is parallel to the plane…

A: To find out equation of plane first we change the equation of line in symmetrical form then find out…

Q: Show that the plane 2x − y − 3z = 4 is parallel to the line x = −2 + 2t, y = −1 + 4t, z = 4, and…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: For what positive value of cc is the acute angle between the plane containing the points A(0,0,1),…

A: According to the given information, it is required to find the positive value of c is the acute…

Q: Find the angle between the planes x+y=D1 and 2x+y-2z%3D2?

A: Given planes : P1: x+y-1=0, P2: 2x+y-2z-2=0 ⇒n1⇀=i+j, n2⇀=2i+j-2k

Q: 25. Determine the distance between the parallel line {y = 5-t, te R and the plane {y = 2-s -t, s,t E…

A:

Q: 1)calculate a*yz dædydz where D is the rectangular parallelepiped 1< « < 2,1 < y < 2,1 < z < 5

A:

Q: Find the cosine of the angle between the planes  x + y + z = 0 and x + 4y + 3z = 2.

A: The two planes be  a1x+b1y+c1z+d1=0a2x+b2y+c2z+d2=0 let the angle between the planes be α  Then cos…

Q: Find the distance between the given parallel planes. 4x – 5y + z = 16, 8x – 10y + 2z = 3

A:

Q: If 0 is the acute angle between the planes x + y = 2 and x + y +2z =v 6, then 2cos (0) = 0 1 O 2 1/2…

A: Angle between planes is defined as angle between their normals.    Option  C is correct answer

Q: Determine the location of a point (x, y, z) that satisfies the condition z = −5

A: The condition is z = −5

Q: If the line L: X = 3 + 2t , Y= 2t , Z=t intersects the plane X+ 3y Z -4 in a point P. The…

A:

Q: 7. Find the dis to the plane x +2y+ 6z = 10 %3D 8. Find the angles between the planes a+y= 1,…

A: According to guidelines we should have been able to solve only one question at a time #8

Q: 9. Find the angle between the two planes 2x + 3y + z = 3 and x + 3y + 2z = -3

A: Given,           2x+3y+z=3    and   x+3y+2z=-3We know that,           Suppose the two equation be…

Q: A) Find the angles between the planes 2 x + 2 y + 2 z = 3 and 2 x - 2 y- z = 5

A:

Q: (2t+l, st-5, lot ) f 4z: Given two lines ( 34, 2++3, zt+1) located in Sice the plane ? plane, find

A: The required equation for the plane is calculating by the below method.

Q: 3. Determine the angle between the planes: x - z+7=0 2x +y-z+8 = 0

A:

Q: what is the intersection of plane  x+2y+z=0 and the line (x,y,z)=(0,1,2)+k(–1,1,2), KER(real…

A:

Q: Find the distance between the planes 4x + 5y + z = 25 and 4x + 5Y + z = 53. %3D

A: Explanation of the solution is given below....

Q: Fud the Line pussing through the posnt (!,-l,o) and purrllel to the Eme of intersection of planes (X…

A:

Q: 02. A. Show that the plane 3x + y - z = 9 and the line {x = 2,y = -1+ 3t ,z = 1+ 3t} are parallel,…

A:

Q: and V is the dosed by the Planes x=0, y=O, ニこ

A:

Q: Find the distance between two skew lines x = 5+t, y = 5 + 3t, z = 4 -t and x = 2t, y =t, z=t O 1 3 '…

A:

Q: 8. What is the angle between the two planes x+y=0 and y-z=2?

A:

Q: Determine the angle between the following two planes: −x + 6y + 3z − 6 = 0 2x + 3z − 10 = 0

A:

Q: Find the angle between the line 2 x+v3 : = z + 1 and the plane vZx + y + z – 2 = 0.

A:

Q: 17. Find the angle between two planes below. a. 2x- y+= =5 and 3x + y-z =1 b. 2x - 4y + 6z = 1 and…

A:

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.