On the line of intersection of the planes y+2z=12 and x+y=6, find the point (a,b,c) that is closest to the origin. What is a+b+c?

Q: Find the equation of the plane through (-1,4,2) and containing the line of intersection of the…

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Q: Determine the geometric location of the points in R3 that equidistant from the plane y = 3 and the…

A: This is question of 3d geometry and locus.

Q: Find an equation for the plane that passes through the point (-7, 10, –8), is parallel to the line x…

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Q: The acute angle of intersection of the planes x + y− 2z = 5and3y −4z = 6 is _____.

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Q: Find an equation of the plane through (-1, 2, -5) and perpendicular to the planes 2x- y+z = 1 and…

A: We are  authorized to answer one question at a time, since you have not mentioned which question you…

Q: Find two different planes whose intersection is the line x = 1 + t, y = 2 - t, z = 3 + 2t. Write…

A: Given:

Q: Find the points in which the line x = 1 + 2t, y =-1 - t, z = 3t meets the three coordinate planes.

A: Given line is  x = 1 + 2t, y =-1 - t, z = 3tWhen the line meets xy plane then z=0So, 3t=0Or, t=0

Q: What angle does the line of intersection of the planes 2x + y - z = 0 and x + y + 2z = 0 make with…

A: Given:The planes 2x + y - z = 0 and x + y + 2z = 0

Q: the Find the distance bebween point of inter Section of the Line %3D X -y -Z =2, 2 x +34 -7Z = -1 |…

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Q: 2) The distance between the parallel planes ax + by + cz + d1 = 0 and |d1-d2| ax+by+cz + d2 = 0 is…

A: We find required equations of plane parallel to given plane.

Q: Find the point on the plane 5x+3y+: =11 that is nearest the origin. What are the values of x, y, and…

A: Given: The equation of plane 5x+3y+z=11, To determine: The point on the plane that is nearest the…

Q: Find the line of intersection of the planes 3x+2y-z=7 and x-4y+2z=0.

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Q: The smaller angle (in degrees) between the planes x + y + z =1 and 2x - y + 2z = 0 is

A: Introduction :

Q: Find two different planes whose intersection is the line x = 1 + t, y = 2 – t, z = 3 + 2t. Write…

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Q: Find the line of intersection of the given planes. 4x + y-z = 0 and 2x - y + 3z 4 %3D

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Q: @/ Find the angle between the planes (x-+y+z=1)and (x-2y+32-1). And find the symmetric equations for…

A: Given equations of planes are x+y+z=1 and x-2y+3z=1 Here, a1=1,b1=1,c1=1 & a2=1,b2=-2,c2=3…

Q: For planes 2x + y – z = 2 and 2x + 3y + 5z = 4,

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Q: (a) Find an equation for the line of intersection between the planes x+3y–z= 2 and 2x –y+2z = 5. (b)…

A: Given: Two planes  x+3y-z=2vector a = <1 , 3 , -1 >2x-y+2z=5vector b = <2 , -1 , 2 >

Q: Find the value of x and y in the rhombus. y° 3x 2x

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Q: What angle does the line of interaction of the planes 2x+y-z = 0 and x+y+2z= 0 make with the…

A: The direction vector of the line of the interaction of the two planes is equal to the cross product…

Q: Find the distance between the parallel planes – 2x + y + z = 0 and 6х — Зу — 3г — 22 — 0. - NOTE:…

A: Find the distance between the parallel planes.

Q: The distance from the point S(7, 7, -6) to the plane 2x + 11y + 10z = 9

A: option C 2215 is correct detailed solution is given below

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 angles between the planes 5x + y - z = 10, x - 2y + 3z = -1

A: Solution -  We have equation of two planes -  Plane 1 -…

Q: Find the line of intersection of the given planes. 4x + y + z = 0 and 2x -y + 3z = 2

A: Given planes are: 4x + y + z = 0 2x - y + 3z = 0 Let us consider, z = t Then we get, 4x + y = -t 2x…

Q: Determine if the three planes -x-5y-5z= 2, 4x -5y +4z = 19 and x +5y - z = - 20 have an intersection…

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Q: Find the line of intersection of the given planes. 3x + 2y + z = ~ 1 and 2x - y + 4z = 5

A: Given: 3x+2y+z=−1                                                      ...(i)2x−y+4z=5…

Q: Find the intersection of the line and plane: 2x + 4y – 3z = 19, r(t) = (-2, 1, –1) +t (1, –1,2)

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Q: Find the angle between the planes 3x-6y – 2z = 15 and 2x +y – 2z = 5

A: Recall: Vector method, cos θ=n1·n2n1n2 We have, n1=3i-6j-2k, n2=2i+j-2k

Q: Find the point closest to the origin on the line of intersection of the planes y + 2z = 12 and x + y…

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Q: Find the distance between the parallel planes – 2x + y + z = 0 and - 10x – 5y – 5z – 11 = 0. - NOTE:…

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Q: Find the distance between the parallel planes P1: 2x – y + 2z +6=0 and P2:6x- 3y+6z- 18 = 0

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Q: Find the point on the plane 4x+5y+x=11 that is nearest to (2,0,1). What are the values for x, y, and…

A: The equation of the plane is

Q: (a) Find an equation for the line of intersection between the planes z+3y-z = 2 and 2x –y+2z = 5.…

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Q: 4 - Find an equation of the Planc perpendicular to each of the planes X-y +2=0 and 2x ty - 4z -5 =0…

A: A detailed solution is given below

Q: Find the angle between the planes x+ y=1 and 2x+у-2z32?

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Q: Find the distance between the two parallel planes 2x + 4y + 12z=7 and x + 2y + 6z= 10.

A: We have to find

Q: The length of the line segment joining the two points of intersection is 3 – x = y = 7+1 With the…

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Q: Find the points of intersection of the line x = 3+2t, y =5+7t, z = -3+t, that is, I(t) = 3+2t, 5+7t,…

A: To determine the intersection of the line with the coordinate planes.

Q: How can we recognize if the two planes were parallel or not

A: Consider the vector equation of the two given planes as, r→·n1→=d1r→·n2→=d2 Here, n1→ and n2→ are…

Q: Find the acute angle (in degrees) between the planes x−4y−2z=1x-4y-2z=1 and −x+3y+z=−8-x+3y+z=-8.

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Q: Find the distance from the point of intersection of liies ( X=t, y=3-3t, =-224) and (x=1+t y=4rt,…

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Q: Find the equation of the line of intersection of the planes 2x+y-2z = 1 and x+2y-z = 4.

A: Planes are 3-dimensional spaces, that contains infinite lines. When two non-parallel planes…

Q: B. If the two planes ax-4y - 9z = 4 and perpendicular. Find the value of a. x-2xy + 3z = 1 are

A: Topic = Geometry

Q: Find the equation of the line of intersection of the planes: x+y+z=1, 2x+y-z=2

A: Given the two planes :   P: x+y+z=1   Q: 2x+y-z=2

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

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

Q: Find the distance between the origin and the intersection line of the planes : 2x+y+z=2 and x+2y+z=3…

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Q: Find the point of intersection between the planes TT :x+y-z =1, n, : 2x – 3y -9z = 10 and n, : x +…

A: The three planes are, π1=x+y-z=1 π2=2x-3y-9z=10 π3=x+2y-3z=-4

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.