Consider the points P3 (а, - 4, - 4) Q=(-5, – 4, – 5) R=(- 1, - 1,- 3) a) Find the value of "a" so that the plane containing P,Q,R is parallel to the plane Зх + 16у - 30z368 a= 5 b) Use the value of "a" found above to write an equation of the plane containing the points P,Q,R

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

A:

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

A:

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

A:

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: Find the points of the intersection of the line x = -2, y = 4+2t, z = -3+t with the xy-plane,…

A:

Q: 9) Find an equation of the plane whose points are equidistance from the point (2,-1,1) to the point…

A:

Q: Explain why the three points (2,3,-1), (8,5-5) and (-1,2,1) do NOT determine a plane. You must…

A: Given problem:- Explain why the three points (2,3,-1), (8,5-5) and (-1,2,1) do NOT determine a…

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

A:

Q: 6. Determine the distance from the point (2, -1, 5) to the plane 3x - 3y + 5z = 8.

A:

Q: Find the points of the intersection of the line x = -2, y = 4+2t, z = -3+t with .the xy-plane,…

A:

Q: Find the distance from the point (-1, 3, -1) to the plane -1x + 2y -5z=1.

A: Given: The point (-1, 3, -1) and the plane -1x+2y-5z=1 To find: The distance.

Q: find the distance between point (-1,1,3) and the plane 5x-5y+3z=25

A:

Q: 10

A:

Q: Find the distance from the point (3, 3, 5) to the plane 3x - 3y + 3z = 5. Leave your answer correct…

A: topic- distance of a point from a plane

Q: Find an equation of the plane consisting of all points that are equidistant from (1, 0, -2) and (3,…

A: Let's assume the coordinates of all the points which are equidistant from a points (1,0,-2) and…

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

A:

Q: Find an equation of the plane whose points are equidistant from (6, -5, 3) and (7,5, 5). 13x + 8z –…

A:

Q: Find the distance between the point (0, 2, 1) and the plane 2x − 6y + 3z = 6

A: Distance between the point x1,y1,z1 and the plane ax+vby+cz+d=0is given by-d=ax1+by1+cz1+da2+b2+c2

Q: Find the distance between the point (-1,–1,2) and the plane 2.x+5y-6z =4

A:

Q: Locate the point of intersection of the plane 2x + y - z = 0 and the line through (4,2,0) that is…

A:

Q: Find the point of intersection of the line through (1, -3, 1) and (3, -10, 5), and the plane given…

A:

Q: Find the point of intersection of the line through (1, -4, 1) and (4, -10, 5), and the plane given…

A:

Q: find the symmetric equation of the line through point (1,-2,-4) which is orthogonal to the plane…

A: We have to find the symmetric equation of the line through point (1,-2,-4) which is orthogonal to…

Q: Find an equation of plane through the points pl (-1, 1, 1) and point of intersection of the plane 2x…

A:

Q: Find the point of intersection of the line through (1, -3, 1) and (3, -12, 6), and the plane given…

A: Given the point (1,-3,1) and (3,-12,6) and the plane x-y+z=6

Q: Find an equation of the plane consisting of all points that are equidistant from (-2, -1, 0) and (0,…

A: Find an equation of the plane consisting of all points that are equidistant from (-2, -1, 0) and (0,…

Q: Find an equation for the plane through point (–8, –9, 3) parallel to the plane 6z + 4y – 2z = -87.…

A:

Q: . Find an equation of a plane passing through the point (3, 4. 0) and containing the line of…

A:

Q: Find the distance between (1,-2, - 1)and the plane through the points (1, 2, 3)and (3 , 2, 1)and…

A: Given information: The plane passes through the points (1, 2, 3) and (3 , 2, 1) and perpendicular to…

Q: find the distance from the point (2,2,3) to the plane 2x+2y+2z=4

A:

Q: Find a plane containing the point (5,8,8) and the line of intersection of the planes -4x 4y+ 6z = 74…

A: We have to find the equation of plane containing the points 5,8,8 and the line of intersection of…

Q: Determine the distance between the point (-1, 2, 1) and the plane 2x +14y -5z = 7.

A: The distance between a point (x1, y1, z1) and a plane Ax+By+Cz=D is given by…

Q: Find the point of intersection of the line through (1, -3, 1) and (3, -10, 5), and the plane given…

A:

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

A:

Q: Find the point at which the line (0, –3, 5) + t(4, –1,2) intersects the plane 4x + 4y – 4z = 0.

A:

Q: between the point and the plane. 43. (1,−2, 3); 2x − 2y + z = 4

A: Given: The point is 1,-2, 3 and the equation of the plane is 2x-2y+z=4 To find the distance between…

Q: Find a plane containing the point ( - 5, - 5, 2) and the line r(t) = (1, - 2, 1) + t(4, 7, 5).

A: First you will find the normal vector to the plane and then find the value of the constant d

Q: Find a plane containing the point (-7,-3,-2) and the line of intersection of the planes 3x – 2y – 3z…

A:

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

A:

Q: Determine the distance between the point (-1, 2, 1) and the plane 2x +14y -5z = 7

A: We know that the distance between a point (x1, y1, z1) and a plane Ax+By+Cz = D is…

Q: What is the equation of the plane containing the points (4,−3,1), (−3,−1,1) and (4,−2,8)? A. 14x…

A: Solve by eq

Q: The distance from the point S(-7, 8, -4) to the plane 10x+2y+11z=2. 20 3 8 15 8 225

A: The equation of the plane is  10x+2y+11z = 2 The point is S-7,8,-4 To evaluate : The distance from…

Q: Find a plane containing the point (-4,4,2) and the line of intersection of the planes -3x + 8y + 2z…

A:

Q: 9) Find an equation of the plane whose points are equidistance from the point (2, -1,1) to the point…

A: find the midpoint  ...............point on the plane

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

A: Find the equation of line and then find its intersection with the plane

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

A:

Q: Find the distance from the point (-1,4,5) to the plane 3x+2y-4z=5?

A:

Q: Find the point of intersection of the line through (1, -3, 1) and (3, -8, 4), and the plane given by…

A:

Q: Find an equation of the plane that passes through the points (-2, 1, 1), (0, 4, 7), and (1,0, –1).…

A: The plane that passes through the point,       -2,1,1, 0,4,7 and 1,0,-1

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.