(3, 4, 2), (–2, 1,0), (0, 2, 1).

Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS where P(-2,1,0) Q(2, 3, 2)…

A:

Q: Find the equetion of the plane contains the line x=3t,y=1+t, z=2t, and parallel to the line of…

A: Equation of linex=3+ , y=1+t , z=2tIn carterian formx-03=y-11=z-02Line passing through 0,1,0 and…

Q: find the plane containing the intersecting lines.  L1: x = t, y = 3 - 3t, z = -2 - t; -inf < t…

A: This question is taken from the planes in which we have to find the plane equation. We can write the…

Q: Q3: Find the distance between the origin and the plane containing the points A(1,1,0), B(-1,0,1) and…

A: Find the distance between the origin and plane containing the points A(1,1,0) , B(-1,0,1) and…

Q: Find the volume of the parallelepiped whose adjacent axes PQ, PR and PS where P (1,-2, 2), Q (1, -1,…

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Q: Find a plane containing the point (7,-8,8) and the line F(t) = +t

A: Given that, the point is 7,-8,8 and the line is r→t=-6,-8,-7+t6,8,4. From the given line, the point…

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: Find the area of the band cut from the paraboloid x2 + y2 - z = 0 by the planes z = 2 and z = 6.

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Q: Find the distance between the plane P:8x+3y+9%= 0 and the point (1,-5,20)

A:

Q: Find a plane through P0(2, 1, -1) and perpendicular to the line of intersection of the planes 2x + y…

A: The directional vectors of the planes are given by (2,1,-1) and (1,2,1)The directional vector of the…

Q: Find the intersection of the planes x + y + z = 1 and 3x − 2y +z = 5.

A: Consider two planes which are not parallel to each other and intersect. Since planes are three…

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: Find the intersection of the line and the plane. x + y + z = 14, r(t) =〈1, 1, 0〉+ t〈0, 2, 4〉

A: Given that, The equation of the line is: x + y + z = 14 And, the equation of the plane is:  r(t)…

Q: 14. Find the volume of the parallelepiped having i + 3j + 2k, 2i + j- k and i- 2j + k be the edges.…

A: The edges of the parallelopiped is given to be a=i+3j+2k, b=2i+j-k, c=i-2j+k. To find the volume.…

Q: Find the distance between the planes 5x - 3y + z = 9 and 5x 3y + z = -2.

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Q: Find the shortest distance, d, from the point (5, 0, -8) to the plane x + y + z = 8. d =

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Q: o Find an equahion for the plane throught (l,-l,3) parallel fo the plane 3x ty+Z =7

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Q: Verify Green's theorem in the plane for M = -2y and N = x , where C is the semi circle x2 + y? = 9,…

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Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS where P(-2,1,0) Q(2,3, 2)…

A:

Q: Find a plane containing the point (-3,3,-3) and the line F(t) = +t

A:

Q: 4. Determine whether the planes are between them. 2x – 3y + 4z = 5; x+ 6y + 4z = 3 parallel,…

A: This question can be solved using the concept of angle between two planes.

Q: Graph the first-octant portion of each plane. x + y + z = 15

A: Given a Plane, x+y+z=15 We need to graph the above plane.

Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS where P(-2, 1, 0) Q(2, 3,…

A:

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 distance from the point Q= (2,2,2) to the line of intersection of the planes x+y+z=1 and…

A: Distance from the point Q(2,2,2) to the line of intersection of planes x + y + z = 1 and x + y = 2

Q: Find the shortest distance, d, from the point (6, 0, -4) to the plane x + y + z = 4.

A: The shortest distance of a point from a plane is said to be along the line perpendicular to the…

Q: Find the distance between the parallel planes – 2z + y + : = 0 and 10z – 5y – 52 – 36 = 0. NOTE:…

A:

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: Find the intersection of the line r(t) = 3t + 2, 1, −7t and the plane 2x − 3y + z = 5.

A: r(t)=3t+2, 1, -7t and the plane 2x-3y+z=5

Q: Зх + 2у + 3z %3D 6

A: Use a graphing utility to plot the graph of 3x+2y+3z=6 .

Q: Find the intersection of the line and plane: 4x + 4y – 3z = 5, r(t) = (1, 1, 1) + t(1, –2, 3) %3D…

A: Given that line and plane are 4x+4y-3z=5  ,rt=1,1,1+t1,-2,3To find :intersection point of line and…

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

A:

Q: e find aplane through Po (2,,,-1) and Perpendicular to the line of Intersection of the planes…

A: Equation of plane

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

A:

Q: Show that the line in which the planes x + 2y - 2z = 5 and 5x - 2y - z = 0 intersect is parallel to…

A: Find the vectors normal to the planes x + 2y - 2z = 5 and 5x - 2y - z = 0.

Q: Find the projection in the ry plane of the curve of intersection of the surfaces 2z2 = r? + y? and…

A: Let's find.

Q: XydA, D is the triangular region with Vertices (0,0), Cu,0], and Cor) SketchD onthe XY planel

A: 8/3

Q: Find the distance between the following parallel planes: (a) 3x – 4y +z=1 and 6x – 8y + 2z =3 (b) –…

A: Solve the above questions.

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: Given the planes (x, y, z) = (0,0, –3) + s(1,1,–2) + t(-2, –-1,3), and x + y + z + 6 = 0 : a) Are…

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Q: Find the shortest distance, d, from the point (10, 0, –6) to the plane x + y + z = 6. d =

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Q: Determine whether the planes are parallel or identical −x + 4y − z = 6, −(5/2)x + 10y − (5/2)z = 15

A: Given information: The planes are −x+4y−z=6, −52x+10y−52z=15. Calculation: The normal vectors that…

Q: Find the distance between the given parallel planes. 2x - 4y + z = 8, 4x - 8y + 2z = 3

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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 volume of the parallelepiped with adjacent edges PQ, PR, and PS where P(-2,1,0) Q(2,3, 2)…

A:

Q: Find the absolute maximum and minimum values of f(r, y) = r-3r-y+12y, closed region D, where D is…

A: Given problem:-  Find the absolute maximum and minimum values of f(x, y) = x²-3x-y³+12y, on the…

Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS where P(-2, 1, 0) 2(2, 3,…

A: Follow next step

Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS where P(-2, 1,0) Q(2, 3, 2)…

A:

Q: Graph the first-octant portion of each plane.y + z = 5

A: y+z=5 We need to graph the first octant portion

Q: -:Q1 Evaluate , (x- 2y) dA, where R is the parallelogram in the xy-plane with vertices (0,0), (4,1),…

A: The objective is to evaluate ∫∫Rx-2ydA where R is the parallelogram in the xy plane with vertices…