An equation of a plane P passes through the point (0,0,-3) and perpendicular to the line L:x = 1-2t, y= 3+4t, z = 5+3t %3D is given by: P: 2x + 4y - 3z = 9 O P: -2x - 4y + 3z = 9 %3D O P: 2x - 4y - 3z 9 O P: 2x - 4y +3z 9

Q: 11) Find the equation of the plane that passes through the point (1, 5, 1) and is perpendicular to…

A: A plane is passing through a point (1,5,1) and is perpendicular to the planes 2x + y - 2z = 2 and x+…

Q: Find a line equation through the point P(3,-1,4) and parallel to the line of intersection of the…

A:

Q: Q1// A :- Find an equation of the plane that passes through point (1,4,3) and contains the line…

A:

Q: The equation of the plane that contains the point (1, 2, 3) and the line x = 4t, y = t, z = t is…

A:

Q: The equation of the plane passing through the point (0, 0, 4) and perpendicular to 4 is: the line 4…

A: Equation of plane

Q: (1) Find an equation for the plane that passes through the point (–1,2,2) and contains the line of…

A: Given: Equation of planes x+y-z=5⇒x+y-z-5=0 and 3x-y+5z=3⇒3x-y+5z-3=0 and point -1,2,2, To find: The…

Q: Example 8: Find the point where the line 2t, and z = -3t intersects the plane x = 1 + t, y = –…

A:

Q: Consider that planes of equations 2x +y - 3z =1 and x+3y +z = -2 a) Show that the planes intersect.…

A:

Q: The Cartesian equations of the line perpendicular to the plane 2x -3y + 4z + 8=0 and passing:…

A:

Q: The point in which the line z = 1– 2t, y = 4+ 5t, z = 3- 3t intersects the plane 3x - 4y-2z -1= %3D…

A:

Q: 6. Find an equation of the plane through point P(2, -4, 2) that contains the line F(t) = (2+ 3t, t,…

A:

Q: Find an equation of the plane that passes through the point (-1, 4, 2) and contains the line of the…

A:

Q: Find the Cartesian equation of the plane through the point (5, 1,0) and parallel to the lines = 2+t,…

A:

Q: 15. Find an equation of the plane through the point (-2, 4, 6) and perpendicular to the line r = t,…

A:

Q: Let Q(0,-1,1) be a point in space and let u have the line L whose equation is L: 3- 3x = 1 – 3 y…

A:

Q: 10) Find the point of intersection of the lines L4:x = 1+ 2t, y = 2 + 3t, z = 3 + 4t and L2: x = 2 +…

A:

Q: Find the equation of a plane through the point (1, – 1, 6) and orthogonal to the line x(t) = 7 + 4t…

A: Required plane is orthogonal to the given line, say L: x(t)=7+4ty(t)=-3-4tz(t)=-1-6t also, the plane…

Q: Consider that planes of equations 2x + y - 3z = 1 and x+ 3y +z = -2 a) Show that the planes…

A:

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

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

Q: Given: planes ¹: 2x - 5y+z=-1 and 2: x + 5y+z=5 intersecting on a line . (a) Determine the symmetric…

A:

Q: which of the following is the equation of the plane that is passing through the point P(2,2,-2) and…

A: Given P( 2, 2, -2) and planes  x+2y-3z=3 and x+y+z=2

Q: Find an equation of the plane through (-8, 6, - 6) that is perpendicular to the planes 9x - y + z =…

A:

Q: The equation of the plane passing through the point A(6, 6, 6) and orthogonal to the line a 11+7t, y…

A:

Q: 1. Find the equation of the plane containing the lines L1 and L2 given below: z = 4t + 3 z = -4s – 1…

A: Given :L1:  x=2t+1, y=3t+2, z=4t+3L2 : x=s+2, y=2s+4, z=-4s-1

Q: Find the symmetric equations of the L that is parallel to the two planes x+y-z= 2 and z + 3y+ z =…

A:

Q: Which of the following is the equation of the plane that is passing through the point P(2, 2, –2)…

A: The equation of the plane passing through the points (x0 , y0 , z0) and perpendicular to a vector…

Q: Given the point P (4, 5,-1) and the line L: x = 3+ 2t ; y=1+3t; =2+t Find the equation of the plane…

A:

Q: 1. Find the equation of the plane that passes through the points P(2,0,1), Q(1,0,-1) and R(3,0,1).

A: We have, Vectors in the plane are, Therefore, equation of plane passes through 3 points will be,…

Q: Find a line equation through the point P(1,2,3) and parallel to the line of intersection of the…

A: We know that the equation of a line passing through the point a and parallel to the vector b is…

Q: The equation of the plane through P.(2, 4, :5) perpendicular to the line :X = 5 +t ,Y= 1+ 3t , Z= 4t…

A: (.)  Let the point Px1,y1,z1 and perpendicular line  x-x0a=y-y0b=z-z0c Then the equation of the…

Q: Which of the following is the equation of the plane that is passing through the point P(2, 2,–2) and…

A:

Q: Find the symmetric equations of the L that is parallel to the two planes x + 2y - z= 2 and x + 6y+ z…

A: Given: Two planes, P1: x+2y-z=2, P2: x+6y+z=-3, Point P1, 2, 3

Q: 6) = Find the point at which the line intersects the given plane. x =3 - t, y = 2 + t, z = 5t; x - y…

A: Equation of a Line in Parametric Form: where are functions of and is the parameter The equation of…

Q: Find an equation of the plane that passes through the point (-1, 4, 2) and contains the line of the…

A: Given data: Intersecting planes are, 4x-y+z-2=02x+y-2z-3=0 Point, x,y,z=-1,4,2

Q: ) Find the equation of the plane passes through the point P(2, 2, 3) and perpendicular to the two…

A: To find the equation of the plane that passes through the point P (2, 2, 3) and perpendicular to the…

Q: Which of the following is the equation of the plane that is passing through the point P(2, 2,-2) and…

A:

Q: 11. z = 1+ 2t 3x + 11y - Find an equation for the plane parallel to the line x = 1-2t, y = 2+3t and…

A:

Q: Find a line equation through the point P(1,2,3) and parallel to the line of intersection of the…

A: Planes as:                       2x+y-z=3x+2y+z=2;   The given point as:                        (1,…

Q: 2) Find the symmetric equation of the line containing the point (1, 2, 1) and perpendicular to the…

A: consider the direction ratio of line  contaning the point ( 1, 2 ,1 )  is  l , m, n

Q: Find an equation of the plane that passes through the point (-1, 4, 2) and contains the line of the…

A:

Q: Which of the following is the equation of the plane that is passing through the point P(2, 2,-2) and…

A: To find the equation of the plane passing through the point P 2,2-2 and vertical to the line of…

Q: 20. The Cartesian equation of the plane which contains the point (1, -2, 3) and perpendicular to x-7…

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Find an equation of a plane containing the line r=⟨0,−5,−1⟩+t⟨−2,4,−2⟩ which is parallel to the…

A:

Q: Find an equation of the plane. The plane that passes through the point (3, 4, 5) and contains the…

A: Calculus Question

Q: The equation of the plane that passes by P(-1, 2, 1) and that is perpendicular to the line x - 3 1-…

A:

Q: Find an equation of the plane that passes through the point (-1, 4, 2) and contains the line of the…

A:

Q: (i) Find the distance from the point P(-1, 2, 1) to the plane II1 : 2x + y – 3z= 4. (ii) Find an…

A:

Q: let L be the line whose symmetric equations are x-1=(y-1)/10=z+1. the equation of the plane through…

A:

Q: Consider that planes of equations 2x +y - 3z =1 and x+3y +z = -2 a) Show that the planes intersect.…

A:

Q: At what point does the line r(t) = (6- 3t)i + (-2 + 2t)j + (-1- 3t)k intersect the yz-plane %3D O a.…

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.