a)What is the distance between the point A(3,1,-1) and the plane 4x + 4y +7z +2=0 ? b) Find the Cartesian equation of the plane containing the points A(4,0,4), B(1,5,5) and C(-1,-1,2).

Q: Find an equation of the plane that is parallel to the plane x + 8y – 4z + 12 = 0 and contains the…

A:

Q: Find an equation of a plane making an angle of π/2 with the plane 3x + y − 4z = 2

A: Here we have to find the equation of plane  making an angle of π/2 with the plane 3x + y − 4z = 2

Q: Find an equation of the plane that is parallel to the plane x + 2y – 4z + 16 = 0 and contains the…

A:

Q: Determine an equation of the plane that contains the point (1, 1, 2) and is parallel to the plane…

A:

Q: Find the angle of intersection of the plane 2x+3y+5z=−32x+3y+5z=−3 with the plane 3x+2y−1z=0

A: Given: - The plane is, 2x+3y+5x=-3, with the plane 3x+2y-z=0 To find: - The angle of intersection of…

Q: Find an equation of the plane that is parallel to the plane x + 4y – 3z + 16 = 0 and contains the…

A:

Q: (b). Determine the equation of the plane that contains the points P(1, –2,0), Q(3, 1, 4) and R(0, 1,…

A:

Q: Find the symmetrical point of point P(-1,-3,5) with respect to the plane D:3x-2y+z+6=0

A: Point P(-1,-3,5)  plane D:3x-2y+z+6=0

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: To find the equation of a plane which cuts intercepts a, b, c res- pectively on the axes of…

A:

Q: Consider the planes of equations −y+z−2=0 and x−y=0. a) Show that the planes intersect. b) Find…

A: We can solve this using definition of intersection of plane

Q: Find the standard form equation (using variables T, y, 2) of the plane P through the points…

A: When a plane passes through 3 points, then equation of the plane is given by-…

Q: M (1; -2; 4) parallel to the OXZ plane

A:

Q: Determine the Cartesian equation of a plane that has x-, y-, and z- intercepts 1/3, 1, and -1/2,…

A:

Q: Find an equation for the plane containing the three points (0, 1, -1), (1,0,1), and (2, 1, 0). Where…

A:

Q: Determine the Cartesian equation of the plane that contains the line = (7,2,-1)+ a(4,5,1) and…

A: Given problem:- Determine the Cartesian equation of the plane that contains the line = (7,2,-1) +…

Q: Find the Cartesian equation of the plane containing the points A(1,0,3), B(1,1,-2) and C(-1,2,0).…

A: Solution

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: Answer the question in the picture.

A: Concept:

Q: 37 Find the equaton of a plane that contains the point (4, -3, –1) and is perpendicular to the…

A:

Q: Find the Cartesian equation of the plane containing the points A(- 1,0, 1), B(2, 1, 3), C(4, – 2,…

A: topic - equation of plane through three points

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: How do you find the parametric and symmetric equation of the line passing through the point (3, 2,…

A: We have to find the parametric and symmetric form of the line perpendicular to the given plane at a…

Q: Determine the Cartesian equation of a plane that passes through a point (2,1,-5) and perpendicular…

A:

Q: Draw a sketch of the plane of 4x – 4y + 2z – 9 = 0. -

A:

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: Determine the equation of the plane containing the points: P (1, 2, -3), Q (2, 3, 1) and R (0, -2,…

A: Vector equation of a plane passing through three points with position vector P→,Q→,R→is given by…

Q: Which of the points A(-4, 0, -1). B(3, 1, -1), and C(2, 4, 6) is closest to the yz-plane? Which…

A:

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: Given: a plane containing the point P(-2, 5, -3) and the line [x, y, z] = [-1,2,5] + s[3, –4,1]…

A:

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

A:

Q: Find a full equation of the plane consisting of all points that are equidistant from (0, 1, -1) and…

A: Given two points,  (0, 1, -1) and (-4, 5, -1)  To find the equation of the plane which is…

Q: You are given the following points: A = (-4, 20, 16), B = (20, 0, 7), C = (8, –15, – 19). %3D Which…

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

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: an equation for the plane consisting of all points that are equidistant from the points (-6, 4, 3)…

A:

Q: 2. The plane with equation: 7 = (1,2,3) + m(1,2,5) + n(1,–1,3) intersects the y- and z- axes at two…

A:

Q: 2) Find an equation of the plane that contains all points that are equidistant from the points…

A:

Q: The general equation of the plane that containsteh points (1,0,3),(-1,1,-3)and the origin is of the…

A: Given general equation of plane is

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 Cartesian equation of the plane containing the points A(1,0,3), B(1,1,-2) and C(-1,2,0).

A:

Q: Find distance from point A(1,2,1) to the plane containing the three points B(2,2,4), C(−1, −2, −3) &…

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

Q: Find an equation of the plane that is parallel to the plane x + 2y – 7z + 15 = 0 and contains the…

A: A detailed solution is given below.

Q: -. Which coordinate plane is closest to the point (7, 3, 8)? Find an equation of the sphere with…

A: we have to find the coordinate plane that is closest to the point 7,3,8 and also find the equation…

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: 5. Cakculate the distance between the point (3. 1. -2) and the plane 2x + y - z+1-0 O 10 /14 O -10…

A: Find the distance between point and plane?  Value of k for det A= -4

Q: Two automobiles are driving on a plane. The first automobile is moving north at 10 m/s and rising 5…

A: Let's consider North as +ve y-axis, East as +ve x-axis, and upward motion to be +ve z-axis. Now, the…

Q: ■ Find distance from point A(1,2,1) to the plane containing the three points B(2,2,4), C(-1, -2, -3)…

A: Distance of a point from plane

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.