) Consider the planes given by the equations 2x – 2y – z = 3, x – 2y + z = 8. (a) Find a vector i 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 intersection of these two planes. This plane is

Q: Find the equation of a plane that is perpendicular to the vector 4 i + 2 j - 2 k and passing through…

A:

Q: A. Find the angle between the planes x+y+z 1 and x-2y+3z 1, and Find symmetric equations for the…

A:

Q: Find the equation of a plane that is perpendicular to the vector – i+ 2j+ 2k and passing through the…

A:

Q: Find parametric equations for the line of intersection of the planes x + 2y + 3z = 4 and 5x + 6y +…

A: Given: x+2y+3z=4   and  5x+6y+7z=8To obtain the parrametric…

Q: Determine whether the planes 5x − 3y + z = 4,  x + 4y + 7z = 1 are parallel, orthogonal, or neither.…

A:

Q: 1. Find an equation of the plane that contains the line r = -2+ 3t, y = 4+2t, z = 3 - t and is…

A: We have to find

Q: What is the distance between the point A(2,5,1) and the plane x + 2y +2z +1=0 ? Answer:

A:

Q: Find an equation of the plane that is parallel to the plane x + 5y−z + 8 = 0 and contains the point…

A: To find the equation of the plane that is parallel to the plane x + 5y−z + 8 = 0 and contains the…

Q: The intersection point of the line that passes through the origin and is perpendicular to the plane…

A:

Q: 4. Find an equation (in point-normal form) of the plane containing the points K, M, and N. 5. Let R…

A: This is a problem of Vector Algebra.

Q: The equation of the plane passing through the point A(8, 10, 9) and orthogonal to the line x = 7+…

A: Given: Point A(8,10,9) Line x=7+8t , y=6+4t , z=5+9t

Q: find the equation of the plane through P(1, 3, 2) that is parallel to the plane 5x - 4y + 3z = 7

A:

Q: Find the equation of the plane perpendicular to the x-axis and passing through the point (3,-3,2)…

A:

Q: The equation of a plane n ·〈x, y,z〉= d is said to be in normal form if n is a unit vector. Show that…

A: Given :           The equation of a plane n . <x, y, z> = d is said to be in normal form if n…

Q: Find the point in which the line X = 2, y = 3 + 2t, z = -2 – 2t; meets the plane 6х + Зу - 4z -12…

A: the point at which the line meets the plane is (x,y,z) = (2,-207,277)explanation is given in below…

Q: (A) Find the Distance between the point (x.y.z) and the plane 3x+2y+6z = 6 If the plane meet with…

A:

Q: a) Show that the shortest distance between the point (a, b, c) and the plane Ax + By + Cz + D = 0 is…

A: Part(a): Given, The point is a,b,c  And, the plane is, Ax+By+cZ+D=0

Q: Find an equation of the plane containing the point (2,1,-1) and parallel to the plane 3x – y + 2z =…

A:

Q: 1. Consider the plane II1 : 3z + 2y + x = 2. (a) If II2 : 2z – 3y = 1 is another plane. Are the…

A: Here we solve the three dimensional geometry problem.

Q: 19. Given that A is the point (5,-1,2), I is the plane with vector equation: r. (2i + 6j + 9k) =…

A: Plane and line.

Q: 2. Find an equation of the plane that contains the line r = 1 +t, y = 2 - t, z = 4 – 3t, and is…

A:

Q: find the equation of the plane with the given description. Passes through O and is parallel to 4x −…

A: Solution:Given    A plane 4x − 9y + z = 3To find the equation of the plane passess through O and is…

Q: Find the symmetrical point of point P(1, 3, 4) with respect to the plane D:3x-2y+z+6=0.

A: Symmetrical point at plane problem....

Q: Let M be a plane that contains the point with coordinates (-2,-2,-1) and is orthogonal to the vector…

A: Let M be a plane that contains the point with coordinates -2, -2, -1 and is orthogonal to the vector…

Q: Find an equation for the plane through the point (3, 4, −4) and parallel to the plane defined by 4x…

A:

Q: Find constants a, b, c such that  G( u, v) = ( u + av, bu + v, 2u - c) parametrizes the plane 3x - 4…

A: Given G( u, v) = ( u + av, bu + v, 2u - c) parametrizes the plane 3x - 4 y + z = 5.

Q: Find an equation of the plane containing the point (2,1,-1) and parallel to the plane 3x – y + 2z =…

A:

Q: Which of the following planes is parallel to the plane 3x – 2y + z= 3? - Oz=3x- 2y + 9 z = 6x- 4y +…

A:

Q: Q1) the plane has equation of 4x-3y-2+5=0 Pud equation of plane partlel to R) and contimons with…

A: Given that: Equation of given plane is: 4x-3y-245=0and contains point (2,1,3)

Q: Find an equation of the plane satisfying the given conditions.

A:

Q: 3. Consider the plane TT: 4x + 3y - 2z + 12 = 0. What is the relationship of the plane to each of…

A:

Q: Suppose P is the plane described by the equation ax+-by + cz + d = 0. Given two points (X0, Y0, Z0)…

A: Given equation of plane ax+by+cz+d=0. The plane ax+by+cz+d=0 will divide the xyz space into two…

Q: 2. Do the two planes intersect? If they do, where do they intersect? TT 2x - y + z = 1 = 0 3 TT 4 x…

A: Equation of the line perpendicular to the given plane be n1 & n2 . Now here n1≠ k n2  , where k…

Q: 7. Find equation of the plane, R passing through points A= (-1, 2, 5) and B= (1, 4, 3) and…

A:

Q: Find the cartesian equation of the plane determined by the two intersecting lines x-4 y+1 z-2 L1: 3…

A: Here,  v1=3i+2j+kv2=5i+3j+2k v1×v2=ijk321532=i4-3-j6-5+k9-10=i-j-k Thus, the equation of the plane…

Q: 12. a. Use vectors to show that the distance from P;(x1, Y1, Z1) to the plane Ax + By + Cz = D is…

A:

Q: 1. Find an equation for the plane through Po (0,2,-1) perpendicular to n = 3i - 2 j- k ?

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Consider the plane P :r+y-z=0 in R that contains both the points P:(1,0,1) and P:(0, 1, 1). Answer…

A: The equation of the straight line passing through 2 points is , , .  Here, the points are .

Q: Let M be a plane with the following properties: • M contains the point with coordinates (-1,-1,0) •…

A:

Q: 2. Write the plane equation when it passes through a point Mo(11,2) and is: a) perpendicular to the…

A: We have to find the equation of the plane.

Q: Find the equation of the plane which passes through O and is parallel to z –- 3x = -2 %3D х+ y + z =

A:

Q: A) Find the point at which the line x = 2, y = 3+ 2t, z = -2-2t meets the !3! plane 6x + 3y- 4z -12

A: Here we have to find the point at which the line x=2, y=3+2t, z=-2-2t meets the plane 6x+3y-4z=-12…

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: Find the angle between the plane -2x +y-2z 0 and the plane generated by the points P1(0, 0, 0),…

A:

Q: Find the cosine of the angle, 0 Ses x/2, between the plane x +2y-2z= 2 and the plane 4y-5x + 3z =…

A:

Q: 4) Find equations for the planes: a. The plane through P(0,2,-1) normal to n = 3i-2j-k

A:

Q: Find the equation of a plane containing Po (1, 2, 3) and perpendicular to n = .

A: We have to find the equation of a plane containing P0 (1,2,3) and perpendicular to n = <1, -1,…

Q: (3) Write the equation of the plane which is perpendicular to the vector ñ² = (2₁-1₁-2) and touches…

A: To find- Write the equation of the plane which is perpendicular to the vector n→ = 2, -1, -2 and…

Q: The equation of the plane passing through the point A(4, 9, 4) and orthogonal to the line a = 9 +…

A: