Find an equation of the plane that passes through the line of intersection of the planes ( x – z = 1 & y – 2z = 3 ) and is perpendicular to the plane x+ y – 2z = 1?

Q: Find the equation of the plane through (1,2,3) and parallel to the plane: x+y=-2-z

A:

Q: Find the equation of the plane containing the line of intersection of the two planes z+y+z+5=0 and…

A:

Q: 20. Find the point at which the line a = 1+ 2t, y = 4t, z = 2 –t intersects the plane r+y – 2z +1=…

A: Given that, equation of line:- x=2t, y=4t, z=2-t Equation of Plane:- x+y-2z+1=0

Q: 32. Find the equation of a plane through the origin and per- pendicular to x – y+ z = 5 and 2x + y–…

A: Note- According to Bartleby guidelines, we are supposed to do only one question. If you want more to…

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

A:

Q: Find the equation of the plane that passes through the point (6, 0, −2) and contains a straight r:…

A:

Q: Find the equation of the plane passing through the point (-1, 4, 0) perpendicular to the line L₁: x=…

A:

Q: Find the coordinates of the point where the line F = (1+ 2t)i + tj – 2tk intersects the plane 2x – y…

A:

Q: Find the point on the plane x − 2y + 3z = 6 that is closest to the point (4,2,0).

A:

Q: Find the equation of the plane through the line of intersection of the planes x+y+z=1and 2x+3y+4z=…

A: The equation of the plane through the intersection of the planes, x+y+z=1 and 2x+3y=4z=5, is…

Q: Find the point P where the line x = 1 + t, y = 2t, z = -3t intersects the plane x + y - z = 0.

A: Given Line is x=1+t,y=2t and z=-3t  And Given plane is x+y-z=0

Q: Find an equation of the plane that contains the line l(t) =(-1,1,2)+t(3,2,4)y which is perpendicular…

A: As given by the question There are given that the equation of line: lt=-1, 1, 2+t3, 2, 4 And, The…

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

A:

Q: Find an equation of the form ar+by+cz = d for the plane that passes through the points A(3,2,0),…

A:

Q: Find the equation of the plane through the line of intersection of the planes x+y+z=1 and…

A:

Q: Find an equation of the plane that is parallel to the plane x + 7y – 2z + 20 = 0 and contains the…

A:

Q: Find the point on the plane x+y+z=-46 that is closest to the point (1,1,1).

A:

Q: Determine the general equation of the plane 2 passing through the point P(1, –4, –5) and parallel to…

A:

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: Find an equation of the plane containing the line = 3t, y=2-4t, z = 1+ t and parallel to z-axis.…

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: Find the point(s) of intersection (if any) of the plane 2x + 3y = 10 and the line (x − 1)/3 = (y +…

A: The equation of line x-13=y+1-2=z-3=r(arbitarary point) then x = 3r +1 y = -2r -1 z = r+3

Q: The line X=t, y+1=t, Z=t intersects the plane. x-2y+Z=2 at the point

A:

Q: Find an equation of the plane containing the point (1,2,-2), and the line: x= 2t, y= 3-t, and z…

A: To find the equation of plane we need to find its normal vector. To find the normal vector, we…

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 general equation of the plane containing the point (2,-1,4) and normal to the line 2 I+3…

A: The equation of the line passing through the points x1,y1,z1 with direction ratios a, b and c is…

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

A: Substitute the line equation in the plane equation

Q: Find the point of the intersection of the plane P: 2x - 3y + 4z + 14 = 0 and the line L:r = 1 – t,…

A: Given the equation of line and plane  2x−3y+4z+14=0x=1−ty=1+tz=2+3t

Q: What is the equation of the plane parallel to 3x + 4y − z = 5 passing through the origin?

A: 3x+4y-z=5

Q: Find the equation of a plane that passes through the point (0,0,0) and contains the line x = 2 -t y…

A: Here we have to find the equation of a plane that passes through the point (0,0,0) and contains the…

Q: Find the equation of the plane perpendicular to the line x 2t, y = 6 - t, z = 4+t and containing the…

A:

Q: Find the equation of a plane through the point(- 3, – 2, 3) and orthogonal to the line x(t) - 5+ 8t…

A:

Q: Find the equation of a plane that passes through the origin and contains the line x = 2t, y = 3t, z…

A: Consider the provided question, The equation of a plane passing through the point (x1, y1, z1) is…

Q: Find an equation of the plane. The plane that passes through the line of intersection of the planes…

A:

Q: Find an equation of the plane through the origin that is parallel to the plane 4x – 3y + 7z + 13 =…

A:

Q: 2. Find an equation of the plane containing the point P (0, -) and the line determined by the two…

A:

Q: Find the general equation of the plane containing the point (2, –1,4) and normal to the line 2 = =…

A: As the line is normal to the plane, the DRs of the line and normal of plane is same.

Q: Find an equation of the plane. The plane that contains the line x = 3 + 2t, y = t, z = 9 – t and is…

A:

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: Find the general equation of the plane that contains the point (2, 0, 3) and the line x =−1+t, y =…

A:

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

A:

Q: Find an equation of the plane containing the line a = 3t, y = 2 – 4t, z = 1+t and parallel to…

A: We have to find the equation of the plane containing the line x=3t, y=2−4t, z=1+t and parallel to…

Q: Find the point on the plane 5x +4y+z 12 that is nearest to (2,0,1). What are the values of x, y, and…

A: The plane 5x+4y+z=12Normal vecor of the plane               <5, 4, 1>The point we seek would…

Q: Find a plane that is perpendicular to the two planes x + y = 3 andX + 2y - Z = 4.

A: Since we have been given two planes x+y=3-(i) and x+2y-z=4-(ii)Our Aim is to find a plane that is…

Q: Find an equation of the plane. The plane that passes through the line of intersection of the planes…

A:

Q: Find an equation of the plane that contains the point (2,0,-8) and contains the line y- 2 z+1 x +4 =…

A: The plane passes through the point 2, 0, -8. Thus, the equation of the plane can be written as…

Q: Find an equation of the plane perpendicular to each of the planes z – y+z = 0 and 2r+y-4z–5 =0 and…

A: The given problem is to find the equation of plane perpendicular to each of the given planes and…

Q: Find an equation of the plane. The plane that contains the line x = 2 + 2t, y = t, z = 6 − t and is…

A:

Q: Give the general form of the equation of the plane that is perpendicular to the plane x+2y x-4 1-2y…

A:

Q: Find the equation of the plane in the form z = c + mx + my containing the line in the xy-plane where…

A: Plane

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.