Write the equation of the plane passing through point (3, 8, 3)| that is parallel to the xz- plane..

Q: Find distance from point (-6, 3, 5) to the plane – 2y – 4z = 8| -

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Q: ) Find the vector that parallel to the intersection line of two planes 2x +y-3z 2 and -x+2y-z 1.

A: Given problem:- Find the vector that parallel to the intersection line of two planes 2x + y - 3z = 2…

Q: Find an equation of the plane through (-7, 2, 1) that is 2 = 3t, y +3 = 6t, z = perpendicular to the…

A: We know that equation of plane passing through the point (x1,y1,z1) and normal n=ai+bj+ck is…

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

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Q: Locate the point of intersection of the plane 2x + y−z = 0 and the line through (3, 1, 0) that is…

A: Our Aim is to locate the point of intersection of the plane 2x+y-z and theline through (3,1,0) that…

Q: write down the equation of the plane. The plane containing the point (1,-5,8) and orthogonal to the…

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Q: Find an equation of the plane through(-4, 4, – 4) that is perpendicular to the planes 9x – y + z = 9…

A: Given,            The plane passes through -4,4,-4 that is perpendicular to the planes…

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

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

A: Given:

Q: find an equation of the plane. The plane that passes through the point  (1, −1, 1)  and contains…

A: The parametric equations of the line x=3y=4z may be re-written as  so that its vector equation is…

Q: Find the distance between the point (-1, 1,-1) and the plane 3x - 5y + 2z = 12

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Q: 10

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Q: Find an equation of the plane containing (1, 5, -1) that is perpendicular to the line of…

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Q: Find an equation of the plane that passes through the point (1, 6, −4) and contains the line:

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Q: Find the distance from the point (3, -4, 2) to the a. xy-plane b. yz-plane  c.xz-plane.

A: a) Distance of (3, -4, 2) from xy plane:On xy plane , z=0. So, This point is 2 units away from the…

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

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Q: Find the point at which the line (-3, 3, 0) + t(-2, –3, –2) intersects the plane -2x – y + 3z = 5.

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Q: Give the general equation of a plane which has point (1,2, -1) together with line with symmetric…

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Q: Find an equation of the plane consisting of all points that are equidistant from (2, 4, 2) and (-2,…

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Q: Find the general form of the equation of the plane with the given characteristics. Passes through…

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

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Q: Find an equation of the plane. The plane through the point (5, -3, -3) and parallel to the plane 4x…

A: We can use the concept of plane in order to solve the given problem.

Q: Find the equation of the plane con taining the points Р(4, -1, 3) Q(1, -2, -1) and R(1, 0, 8)

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Q: Find the equation of the plane through (-3, 8, -8) that is perpendicular to the plane 7x – y + z = 2…

A: For solving This question I found direction cosine using dot product as two perpendicular plane is…

Q: Find the distance from the point (-6,2,-7) to the plane -x + 4y = 2z = 22.

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Q: Find the point at which the line 7(t) = (5, – 3, - 6) + t( – 2, - 8, 6) intersects the xz plane.

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Q: What is the equation of the plane through the point (4, -2, 3) and parallel to the plane 3x - 7z =…

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Q: Find the equation of the plane passing through (2, 0, 1) and (-1, 2, 0) and perpendicular to the…

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Q: Find the vector that parallel to the intersection line of two planes 2x +y-3z 2 and -x+2y-z 1.

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Q: Find the distance from the point (-5, –13,6) to the plane –9x + 3y – 8z = -67. Distance is ...

A: Given:            point a(-5,-13,6)=(x0,y0,z0)            plane equation is -9x+3y-8z+67=0we know…

Q: Find the equation of the plane that passes through the points A = (1, –4, –1), В - (-5, —3, —5), and…

A: Proceed as shown below

Q: the distance between point and our plane is (-3, 3, -2) and not (-3, -3, -2)?

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Q: Find the point of intersection of the line through (1, -4, 1) and (4, -12, 6), and the plane given…

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

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Q: What is the distance between the point A(1,-1,3) and the plane x + 2y + 2z + 1=0 ?

A: To find The diatance between the point A(1,-1,3) and the given plane

Q: Find equation of the plane through (1,0,-1).(-1,2, 1) and parallel to the line of intersection of…

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Q: How to find an equation of a plane through a specific point such as (3,0,3)?

A: There can be infinitely many planes passing through one point and hence you can not find an equation…

Q: Write the equation of the plane passing through point (3, 8, 3) that is parallel to the xz-plane.. X…

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Q: 4. Determine the equation of the plane passing through the point (1, -4, 3) and parallel to the…

A: We have to find an equation of the plane passing through the point (1, -4, 3) and parallel to the…

Q: 2. Obtain an equation for a plane a that includes straight line(2--5) and 1: point(-2,1,1)

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Q: Find an equation of the plane through (-8, 4, –9) that is perpendicular to the planes 5x – y +z = 1…

A: Solution of question is written in below steps.

Q: Find the equation of the plane through (-6,5,-1) and is parallel to the xy plane

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Q: Find the points at which the line that passes through (–6,6,4) and (12,–6,2) intersects the three…

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Q: Find the equation of the plane through the point (-3,2,0) and perpendicular to the vector (1, -2,5).…

A: Questions from vector calculus.

Q: Find an equation of the plane consisting of all points that are equidistant from (-1, 3, 2) and (2,…

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Q: Find the general equation of the plane through the point (3, 2, 5) that is parallel to the plane…

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Q: Find an equation of a plane through the point (-2, 1, 5) which is orthogonal to the line 2= -3- 3t,…

A: The director vector of the line is (-3, -4, -3). Given that the plane is orthogonal to the line. So…

Q: Where does the line through (-3, 1, 0) and (-1, 7, 4) intersect the plane 2x + y -z = -2?

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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.