In Exercises 33 and 34, find the distance from the point to the plane.33. (6, 0, -6), x - y = 434. (3, 0, 10), 2x + 3y + z = 2

Q: Which of the points A(9, 0, 3), B(6, 5, 6), and C(2, 9, 2) is closest to the yz-plane? Which point…

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

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Q: nd the distance from the point to the plane.   (3,3,8)​, 7y+3

A: Given, the equation of plane is                                       7y+3z=0and  point (3, 3, 8)

Q: Find the angles between the planes x + y = 1, 2x + y - 2z = 2

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

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

A: Given problem:- Find the point of intersection of the line through (1,-3, 1) and (3,-12, 6), and the…

Q: What is the distance between the point A(2,5,1) and the plane x + 2y +2z +1=0 ? Answer:

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Q: Find an equation of the plane. The plane through the point (8, -8, -8) and parallel to the plane 5x…

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Q: Show that the distance between the parallel planes                                          ax + by…

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Q: Find the distance from the point to the plane.   (4,1,8)​, 7y+5z=0

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Q: What is the distance between points (5, 2) and (1, -3) on a coordinate plane? 4.1 © 8.5 6.4

A: We can use distance formula to find distance between two points (x1,y1) and (x2,y2).

Q: Find the exact value of the distance between the line of intersection of the planes 2x-y+2z 6,…

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Q: Find the distance of the point (3,8,2) from the line , -y+3 -z+2 Q2: measured parallel to the plane…

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

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Q: n Exercises 39–41, find the distance from the point to the plane. 39. (2, 2, 3), 2x + y + 2z = 4 40.…

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Q: Find the distance from point P(2, 7, -6) to the plane of equation 5x - y + 4z - 8 = 0

A: We have to find distance

Q: The distance between the point ( 9,8,3) and the plane x + y – 2z = 5 is .... %3D

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Q: Find the intersection of the line and the plane. 2x + y = 3, r(t) =〈2, -1, -1〉+ t〈1, 2, -4〉

A: We have to find the intersection of the plane 2x+y=3 and the straight line r(t)=2,-1,-1+t1,2,-4

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

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Q: Sketch the translation of the triangle with the rule (x, y) → (x+5, y+1). T 5- -10 -5 10 -5- 5

A: The coordinates of vertices of the blue triangle (1st quadrant) are A1, 1, B3, 1 and C3, 5. Now, Use…

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

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Q: Find the point on the plane −2 x+y−z =−9 that is closest to the point (3,−2,2) .

A: We have to find a point on the plane closest to another point.

Q: Exercises 57–60, find the point in which the line meets the plane. 57. x = 1 - t, y = 3t, z = 1 + t;…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find the equation for the plane through the points Po(-3,- 2, – 4), Qo(2,1,3), and Ro(3, - 2, – 5).…

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Q: Find an equation of the plane. The plane through the point (6, −8, −8) and parallel to the plane…

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Q: Find the distance between the point (2, 8, 4) and the plane 2x + y + z = 5.

A: we have to find the distance between the point (2,8,4) and the plane 2x+y+z=5. as we know that the…

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

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Q: Where does the line through (-3, 1, 0) and (−1, 3, 8) intersect the plane 2x + y − z = -2? (x, y, z)…

A: Given the points (-3,1,0) and (-1,3,8) and the plane 2x+y-z=-2

Q: n Exercises 39–41, find the distance from the point to the plane. 39. (2, -3, 4), x + 2y + 2z = 13…

A: Given, (2, -3, 4), x + 2y + 2z = 13.

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

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Q: Which of the points A(-4,0,–1), B(3,1,–5), and C(2,4, 6) is closest to the yz-plan Which point lies…

A: Given: A(-4,0,-1)  B(3,1,-5)  and C(2,4,6) To find: Which is closet to the yz plane Which is lies on…

Q: 3. What is the distance from the line to the plane? 7-(2,3,8)+(1.1.1) 2x - 5y + 32 + 10

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Q: In Exercises 41-44, find the intersection of the line and the plane.42. 2x + y = 3, r(t) = (2, -1,…

A: Given: To find the intersection of the line and the plane.2 x + y = 3,  r(t) = (2, -1, -1) + t (1,2,…

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

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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: 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: In Exercises 41-44, find the intersection of the line and the plane.43. z = 12, r(t) = t (-6, 9, 36)

A: the line we get  r(t) = (-6t, 9t, 36t) x = -6t y = 9t z = 36t

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

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Q: Find an equation of the largest sphere contained in the cube determined by the planes a 1, a = 7, y…

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Q: Find the distance from the point (1, -2, 4) to the given plane 3x + 2y + 6z = 5 Thank you.

A: To find the distance from the point (1, -2, 4) to the given plane 3x + 2y + 6z = 5

Q: Find the distance from the point to the plane. (6, 0, —6), т — у %3D 4

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

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Q: Find the distance from the point (-2, 1, 4) to the plane y = -5

A: Given plane is: y = -5 Given point is: (-2, 1, 4) We know that the distance (d) of a point P(h, j,…

Q: The acute angle of intersection of yz plane and the plane 2x-y+z-4=0 is:

A: Let A1x+B1y+C1z+D1=0 and A2x+B2y+C2z+D2=0 be the equation of two planes aligned to each other at an…

Q: 4] Find the equation of the plane that contains the point (а, 0, 0), (0, b, 0) and (0, 0, c).

A: First find two vector and then take cross product which is normal vector  Now use equation of plane

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

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

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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.