15. Find an equation of the plane through the point (-2, 4, 6) and perpendicular to the line r = t, y = 1- 2t, z = 3 +t

Q: Find the equation of the plane with the given description. Passes through (6, 1, 5) and is parallel…

A:

Q: 1. Find the equation of the plane that contains the point (-1, 1, 2) and the line given by x=1-t,…

A: This question is based on 3d geometry.

Q: Find the point at which the line T(t) = (4, 1, 7) +t( – 5, – 7, – 4) intersects the yz plane.

A:

Q: 5. Determine the equation of the plane that contains the point (0,3,0) and the X = 1 line y = 2t z =…

A:

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: The equation of the plane that passes by P(2,0, -1) and that is perpendicular to the line x-5 2-y Z…

A: The plane passes by P2,0,-1 and that is perpendicular to the line x-5-2=2-y4=z-23

Q: Find the equation for the plane through Po(-6,3,7) perpendicular to the following line. x= -6+t, y…

A:

Q: 2.) Find the Symmetric form of the equation of the line of in tersection of the two Planes X-Y +Z…

A: Let a, b and c be the direction ratios of the required line. Since the required line lies in both…

Q: Find the point of intersection of the line with equation L: (x,y,z) = (1, - 1,0) + t(1,1,2) and the…

A: At the point of intersection the point will satisfy the equation of both line and the plane. So…

Q: Find an equation of the plane that contains the point P(5,0,2) and the line x = 3t +1, y=-2t + 4, z…

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: Find the equation of the plane parallel to the intersecting lines (1,2 +t, -3 – 3t) and (1 – t, 2 –…

A: Let, the direction vector of 1,2+t,-3-3t is v1=0,1,-3 and the direction vector of 1-t,2-3t,-3-2t is…

Q: Where does the line through (1,0, 1) and (4,– 2,2) intersect the plane x+y+z = 6?

A: It can be assumed that the vector for the coordinate 1,0,1 is 1,0,1 and the vector for the…

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: 6. Find the equation of the plane that passes through (3,1,2) and (-1,2,–1) and is parallel to the…

A:

Q: 1. Find the distance from the point S(2,-3,4) to the plane x+2y+ 2z =13

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

Q: 16- Find the equation of the plane that contains the line = 2+ = 5-z, and the point P(0,5,2).

A:

Q: 4) Find the equation of the plane that passes through the point (6,0, 2) and contains the line x = 4…

A: The plane that passes through the point (6, 0, 2) and contains the line x = 4 − 2t, y = 3 + 5t, z =…

Q: I need the answer as soon as possible

A:

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

A:

Q: Find an equation of the plane through (0, –9, –1) that is perpendicular to the line x – 2 = 3t, y +…

A:

Q: 4. Give the general equation of the plane containing the point (3,-1,4) and 2- z perpendicular to…

A:

Q: equation

A:

Q: Find the equation of the plane that contains point P1(1,0,3) and orthogonal to line L1:(5t – 1,3 –…

A: Consider the line L1given by the vector form: L1:5t-1, 3-2t, t    :-1+5t, 3-2t, 0+t    :-1, 3, 0+5t,…

Q: (b) Calculate the distance from the point P(3,–1, 2) to the plane with equation 2x – y +z = 4.

A:

Q: Find equations of the line through the point (1, −1, 1) perpendicular to the line 3x = 2y = z and…

A:

Q: Find the point of intersection of the line x-9 = - 5t, y +1= -t, and the plane 2x – 3y + 4z + 7 =0-…

A:

Q: 7. Find the distance between the point (3, 1, –2) and the plane x + 2y – 2z = 4.

A: Given that plane x+2y-2z=4 and point 3,1,-2To find :Distance between point and plane Solution if…

Q: 4. Write the equation of the plane parallel to the z-axis, with xy-trace x + y - 2 = 0.

A: Write the equation of the plane parallel to z axis, with xy trace x+y-2=0.

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: Determine the equation of the plane through the points (1, 0, 3) and the line l : ¯r = (3, 4, 1) +…

A:

Q: 25. Find an equation of the plane through the line of intersection of the planes x – z = 1 and y +…

A: Equation of a plane P that passes through the line of intersection of two planes P1 and P2 is given…

Q: 1. Determine the point of intersection between the line, L: x = 3+t, y=4-5t, z=1-7t, te R, and the…

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

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: Find the point at which the line (4, –1, 4) + t(4, 2, 3) intersects the plane 4x 5y + z = 88.

A:

Q: Find an equation of the plane through (1,8, 5) that is perpendicular to the line x – 2 = 3t, y + 3 =…

A:

Q: Find the general equation of the plane perpendicular to the line z – 2 y + 4 1- x = 3 and is 3…

A: We have to find the equation of plane.

Q: d. The plane through P,(2,4,5) perpendicular to the line x=5+t y=1+3t .

A:

Q: Find the general equation of the plane perpendicular to the line Z – 2 y+ 4 1- x = 3 and is 3…

A: This is a problem of vector algebra and geometry.

Q: The intersection point of the line whose equation is (x+2y+z=1),(x+y+2z=-1) with the xz plane is: O…

A: Here the two equation are: x+2y+z=1x+y+2z=-1

Q: 4. Find the equation of the plane that contains the intersecting lines a = 4 +t1, y = 2t1, z =1-3t…

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

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 the shortest distance between (3,4,1 ) and the plane X+y +Z = -2

A: Using distance between plane and point formula we can calculate.

Q: 16- Find the equation of the plane that contains the line = 5 - z, and the %3D point P( 0,5,2).

A:

Q: A normal equation of the plane that contains the line 1₁: (x, y, z) = (1, -1, 2) + t (9, 1, 3), t E…

A:

Q: Find the equation of the plane that passes through the point (1,0,-2) and contains the line with…

A:

Q: 12. Find the distance between the point (3,-2,7) and the plane 4x – 6 y + z = 5.

A: The equation of plane is 4x-6y+z=5 and the given point is 3,-2,7. The distance between the point and…

Q: what is the equation of the plane perpendicular to the intersection line of the x-2y+2z= 3  and…

A:

Q: 1. Determine the point of intersection of the line and the plane if it exists. π: 7x+y+ 5z = 0 x-4…

A:

Q: Find the equation of the plane that contains the point P(3,5, –1) and the line = 4 – t, y = –1+ 2t,…

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.