Find the point on the plane 2x + 3y + z =7 that is nearest to (2,0,1). What are the values of x, y, and z for the point? x = y = (Type integers or simplified fractions.)

Q: Find the point on the plane 5x + 4y + z = 11 that is nearest the origin. What are the values of x,…

A: First we find the distance(d) between a point (x,y,z) on the plane and the origin .Then form a…

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

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Q: 5. What is the angle between the planes 4x - 5z 11 and 8x- 10z 13? (a) 0 (c) (b) (d) n

A: Given: 4x-5z=11 8x-10z=13

Q: Find the distance between the planes 5x- 3y +z = 6 and 5x-3y +z = -7. Need Help? Read It

A: Distance between parallel planes

Q: The distance from (9,-6, 7) to yZ-plane is A9 O B. 6 OC. 166 OD. 85 O E.7

A: Distance of a point (a,b,c) from yz plane is as In yz plane x coordinate is zero and y= b and z= c.…

Q: Consider the planes below: ⊼(pie): x+2y–1z=0 ⊼: –x+2y–3z–4=0 ⊼: x+6y–5z–4=0 a) Without solving…

A: Given : x+2y–1z=0 –x+2y–3z–4=0 x+6y–5z–4=0

Q: Among all the points on the graph of z = 6 - x2 – y2 that lie above the plane x+ 3y + 5z = 0, find…

A: Use the distance formula from a point to the plane and then proceed as shown below.

Q: Evaluate x² zdS, where S is the part of the plane z = 3 + 4x + y above the rectangle [0, 4] × [0,…

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Q: 5. The ends of the transverse axis are at (+8,0) and the ends of the conjugate axis are at (0. 16).

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Q: Evaluate / x2 zdS, where S is the part of the plane z = 4+ 3x + y above the rectangle [0, 4] x [0,…

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Q: 1.Find the area of the triangle in the xy-plane with vertices A(n,,n2, n2),B(m,,m2,m3),C(r,,r2, 13).

A: Please see the explanation below

Q: the distance between the two skew lines L and L2. L: x=3+3t, y=-1-4t, z=4+2t. L2: x=6+5p, y=3-p,…

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

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Q: Find the dimensions of the largest rectangular box in the first octant (x, y, z > 0) with one corner…

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Q: 4. Find the angle made between the two planes: r+ y - z = 5 and 2r + y +3z = -1.

A: Given that: Equation of first plane: x+y-z=5   ........(1)Equation of 2nd plane: 2x+y+3z=-1…

Q: 8. The distance between the planes 2r -y-2z 5 and 2r - y- 2z = 7 is A C 2 D 4

A: As the planes are parallel than for calculation distance between planes we use formula:…

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

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Q: Among all the points on the graph of z = 11-x² - y? that lie above the plane x+ 5y + 6z = 0, find…

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Q: Among all rectangular solids defined by the inequalities 0sxsa, Osysb, 0szs 1, find the one for…

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Q: The distance from (4,-5, 10) to yZ-plane is O A.4 O B. 5 C. /141 OD.10 OE. 125

A: Solution is given below:

Q: Find the acute angle of intersection between the two planes 2x−4y + 4z = 6 and 6x + 2y−3z = 4

A: We know that, acute angle between the lines a1x+b1y+c1z=d1 and a2x+b2x+c2z=d2 is given as…

Q: 45. Find the distance from the plane x + 2y + 6z = 1 to the plane x + 2y + 6z = 10.

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Q: 1 Find the angle between the bris 2 • surfaces 4x+98 +32 = 91 and 9 2 = 12- (x²7 y ²) at the point…

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Q: Find the angle between the two planes 2x + 3y + z = 3 and x + 3y + 2z = -3

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Q: Find the acute angle (in degrees) between the planes 5x 4y – 2z = 8 and 5x 2y – 5z = 5. %3D %3D

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Q: Evaluate // x² zdS, where S is the part of the S 1 + 4x + 3y above the rectangle plane z = [о, 2] x…

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Q: Determine the angle between the planes: x-z+7=0 2x +y-z+8 = 0

A: Solution :--

Q: Find the distance between the planes M: 3x – 4y + z – 17 = 0 and N: 6x – 8y + 2z + 68 = 0.

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Q: 8. Find the angles between the planes r+y = 1, 2x+ y – 2z = 2

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Q: A) Find the angles between the planes 2 x + 2 y + 2 z = 3 and 2 x - 2 y-z = 5

A: Given : 2x+2y+2z=3 and 2x-2y-z=5   To find: Angle between planes   we know that for plane Ax+By+Cz=d…

Q: Find the distance between the planes – 3x + 5y = 32 and – 3x + 5y = 27.

A: Simply use the formula for the distance between two planes.

Q: 9. Find the angle between the two planes 2x + 3y + z = 3 and x + 3y + 2z = -3

A: Given,           2x+3y+z=3    and   x+3y+2z=-3We know that,           Suppose the two equation be…

Q: The part of the plane 2x 5y + z = 10 that lies above the triangle with vertices (0, 0), (0, 6), and…

A: Double integration need to be done.

Q: A) Find the angles between the planes 2 x + 2 y + 2 z = 3 and 2 x - 2 y- z = 5

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Q: Find the coordinates of the midpoint of MN with endpoints M(-2, 6) and N(8, 0).

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Q: Among all the points on the graph of z = 10-x2 -y² that lie above the plane r+2y+3z = 0, ind the…

A: Given that z=10-x2-y2 and x+2y+3z=0 Find the point which is farthest from the plane.

Q: 3. Determine the angle between the planes: x - z+7=0 2x +y-z+8 = 0

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Q: 18. Find the point on the plane 2x + 5y +z= 10 that is nearest to (2,0,1). What are the values of x,…

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: The wedge cut from the cylinder, x2 + y? =1 by the planes, z = -y and z = 0. Set up only

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Q: 7. C is the hexagon in the xy-plane with vertices (5, –5), (5,5), (0, 10), (–5, 5), (-5, –5), and…

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Q: Find the area of on of the triangle that can drawn between the planes 3x – 6y – 2z = 15 - and 2r + y…

A: For any triangle that will lie between two planes, one point has to lie on a plane and the other two…

Q: 8. Find the angles between the planes r + y = 1, 2x + y – 2z = 2

A: We will use direct formula to find the angle. The detailed solution is as follows below:

Q: Enclosed by the cylinders z= x2 y = x 2 and the planes  z =0 y =4

A: Given: The cylinders z= x2 y = x 2 and the planes  z =0 y =4 The solid enclosed by the surfaces,

Q: *15. What is the name for the point on the coordinate plane that has the (Inv. 7) coordinates (0,…

A: The given point is: (0, 0)

Q: ce cut from the first octant by the cylinder z = 12 – 3y, and the plane x + y = 2

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Q: Find the distance between the planes M: 3x – 4y + z – 17 = 0 and N: 6x – 8y + 2z + 68 = 0. %3D

A: Distance between parallel planes d=(d2-d1) /(sqrt(a2+b2+c2)

Q: 5. What is the angle between the planes 4x – 5z = 11 and 8x – 10z = 13? (0) (a) 0 (b) 프 (d) π

A: Given: To explain the correct option is given as,

Q: 4 2 + Find the area of the portion of the Sphere x² + y² +2²= 9 between the planes Z=1 and 2 = 0.…

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Q: Among all the points on the graph of z= 11-x²-y² that lie above the plane x+ 5y + 6z = 0, find the…

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Q: To describe the triangular region whose vertices are (0,0), (2,2), and (-2,2) we use the following…

A: We have to describe the triangular region whose vertices are 0,0,2,2 and -2,2