A) Find the point at which the line x = 2, y = 3+ 2t, z = -2-2t meets the !3! plane 6x + 3y- 4z -12

Q: Find an equation for the plane in R³ spanned by the points (1,5,

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

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Q: 3. The plane in ' with equation 4x=34 %3D

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Q: Find the intersection of the plane: x - z = 6, and the line r(t) = (1,0, -,1) + t(4,9,2)

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Q: 8. Determine the Cartesian equation of the plane that contains the line 7=(2, 3. 2) + 1, 1.4), te R.…

A: According to guidelines we solve one question.thanku

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 distance between the point (3,4,5) and the plane 2x + 4y 3z = 12.

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Q: Find the point(s) on the plane 4x +3y +z = 2 that are closest to (1,-1,1).

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Q: 1 2x 3y + z = 0 and 2 +t - 1 1

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Q: Prove that the line x +1 = 글(-6) - lies in the plane 3x + y – 2 = 3.

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Q: 2. ( eMsa lan--a22 3. All 2-tuples representing points in the first quadrant of the plane including…

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Q: Find the distance of point A(1,0,2) to the plane 3x+y+z=9?

A: Here we have to find the distance from the point A(1,0,2) to the plane 3x+y+z-9=0

Q: b. Find the distance from the point (2, –2, 3) to the intersection of the planes 2x – y + 3z = 1 and…

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Q: (42) is the distance between the point (1, –3, –2) and the plane x- 4y-3z-2= 0.

A: In this question we have to find the distance between point and plane. Note: As per our policy we…

Q: 16- Find the equation of the plane that contains the line = 2+ = 5-z, and the point P(0,5,2).

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Q: 4. Find a plane through Po(2, 1, –1) and perpendicular to the line of in- tersection of the planes…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Find the distance (d) from the point (– 6, – 8, – 7) to the plane 5x – 2y + 2z = 25. - d =

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Q: Determine the general cquation of the plane 2 passing through the point P(1,-4,-5) and parallel to…

A: We have to find equation of ohm plane

Q: Find an equation for the plane through P(1,4, 4) that contains the line of intersection of the…

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Q: show that the points AC!,l,4) B(2,2,2), coplanear (in the c(o,l,5) and D (1,0,5) are Same plane).

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Q: Find the point in which the line X = 2, y = 3 + 2t, z = -2 – 2t; meets the plane 6х + Зу - 4z -12…

A: the point at which the line meets the plane is (x,y,z) = (2,-207,277)explanation is given in below…

Q: Find the distance between the point (2, -4, 3) and the plane 5x – 2y + z = 10.

A: Given,           The distance between the point 2,-4,3 and the plane 5x-2y+z=10.We know that,…

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

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Q: What is the real number a that makes the line 2 -1 y-12 z-7 a -2 3 parallel to the plane z -y - 2z=…

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

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Q: (31) Find a plane through A(2, 1, –1) and perpendicular to the line of intersection of the planes 2x…

A: Given, 2x+y-z=3 ,x+2y+z=2 The equation of the plane passing through x1,y1,z1 is given by…

Q: Prove that quadrilateral GHIJ with the vertices G(-2,2), H(3,4), 1(8,2), and J(3,0) is a rhombus. YT…

A: solution: the objective is to determine whether the given vertices forms a rhombus

Q: Find the equation of the plane that contains point P(1, -1, 2) and has the normol n= 2¿+3j+Sk.

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Q: If the image of the point (1 -2 3) in the plane 2x+3y-z=7 is the point x, y, z then the value of…

A: Let's first understand the

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: Find the general quation of plane containing the point P(-1,3,3), and perpendicular to the line…

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Q: Find the equation of the plane containing the point (4, -1, 3) that is parallel to the plane 2x - 3y…

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

A: Given, plane z=-1 and the point (-2,1,4)we have to find the distance from the given point to the…

Q: 6) Find the distance between the point (1, -4, -3) and the plane 2x – 3y + 6z = - 1.

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Q: 2. Use analytic geometry to verify that quadrilateral JKLM is a parallelogran 1C). YA K(-1,1) 2 -2 0…

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Q: 2-The distance between the point (2,3,1) and the plane 5x – 2y – 4z = 0 А- 0, В- 6.7, C- V45. is

A: Here, the distance between the given plane and point is zero. Because, the point is on the plane.

Q: 5. Calculate the distance between the point (3, 1, -2) and the plane 2x + y-2+1. O 10 o -10 V14 O 10…

A: The equation of the plane is  2x+y-z+1 = 0 The point is x0,y0,z0 =3,1,-2 To evaluate : The distance…

Q: 5. Find a plane through the points P(1,2, 3), P2(3, 2, 1) and perpendicu- lar to the plane 4x – y+…

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Q: The planes 3x + 6z = 1 and 2x + 2y - z = 3 intersect in a line. Show that the planes are orthogonal.

A: Given: 3x+6z=12x+2y−z=3

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

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Q: 16- Find the equation of the plane that contains the line = 5 - z, and the %3D point P( 0,5,2).

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Q: 1) Find the distance from the point (1, 2, 3) (a) XZ plane to the (b) Z axis

A: In this question we will use basic of geometry i.e concept of 3D geometry. We will first plot the…

Q: 02. A. Show that the plane 3x + y - z = 9 and the line {x = 2,y = -1+ 3t ,z = 1+ 3t} are parallel,…

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Q: The plane containing the point (-4,1,3) and parallel to the plane 4x + 7y – 3z = 2 has equation Ar +…

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Q: Find the equation of a plane containing Po (1, 2, 3) and perpendicular to n = .

A: We have to find the equation of a plane containing P0 (1,2,3) and perpendicular to n = <1, -1,…

Q: Which of the points A(−4, 0, −1), B(3, 1, −5), and C(2, 4, 6) is closest to the yz-plane? Which…

A: Given- A(−4, 0, −1), B(3, 1, −5), and C(2, 4, 6) To do- 1.Which of the points A(−4, 0, −1), B(3, 1,…

Q: Find a plane through the point Po(2, 1, -1) and perpendicular to the line of intersection of the…

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Q: Find the distance between the point Q (3, –2, 4) and the plane 2x – 5y + z = 10 -

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

A: To find the distance

Q: Are the plane 2x-y-4z 10 and the line {x = 2+4t,y 5- 2t,z =-8t} parallel or orthogonal?

A: We have to find out