The Line LI : %3D Plane X+ 3y-Z= -3 , P and intersect the %3D Lind the point of intersection Irne in Ehe equations of the this plane that passes through pand perpendicular to LI

Q: We have two planes in IR, defined by equations I- 3y+z -7 and 2 +y+2z = 0. These two planes…

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Q: •H G a.) Name four points that are coplanar. b.) Name the intersection of plane P and Plane R: c)…

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Q: P5/ Find the Pl0,2,-1) and normal to n= 31-2-k squahion tor the plane through

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Q: (iii) The line segment x = y - 1,0 < y< 1 is revolved about the y-axis to generate the cone shown in…

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Q: 4. Axis of symmetry x 7, directrix y = 0, vertex is on r-y 4 %3D 5. Endpoints of latus rectum (-2,1)…

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Q: Cube ABCDEFGH is given with the side length a. A plane passing through the diagonal AC and thought…

A: Given- Cube ABCDEFGH is given with the side length a. A plane passing through the diagonal AC and…

Q: 5. Find the volume of water in a swimming pool with vertical ends and sides. The length measured at…

A: Given top of pool is of 5ft length and 20ft breadth,    The bottom is sloping gradually…

Q: Line Li: 0.5C1- X)= 2 = 0.5z intersects the plane defined by B(2,237), C Cl,o, 12) at point P. Find…

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Q: The distance between the parallel planes ax + by + cz + dq = 0 and ax + by + cz + dz = 0 D = a² + b2…

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Q: equation of the family of plane of curves in Mdx + Ndy format. 1. Straight lines through the fixed…

A: We are authorized to solve only one question, please repost remaining questions Differential…

Q: The surface S i parametrized by equations x = u + v, y = 3u², z = u – v; The point P (2, 3, 0) lies…

A: Given that the surface S is parameterized by equations x=u+v, y=3u2,z=u-v; the point P(2,3,0) lies…

Q: The plane region is revolved completely about the given line to sweep out a solid of revolution.…

A: Given diagram is                                           shaded area is rotated about x axis. it…

Q: y The plane = 1 intersects the x-, y-, and z-axes in points P, Q, R. Find the area of the triangle…

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Q: Displacement d→1 is in the yz plane 62.8 o from the positive direction of the y axis, has a positive…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Distance between two points P (x = 2, y = 3, z = -1) and Q(r = 10, 0 = 30 , q =60) %3D

A: We have to find the distance between the points P and Q.

Q: surface 7 (u, v), identify the shape of the grid curves when v is constant. apes may be used more…

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Q: Intercepts Let a, b, c, and d be constants. Find the points at which the plane ax + by + cz = d…

A: Given plane ax+by+cz=d where a ,b, c and d are constants.

Q: Lecture I skeleton Example Find the equation (ie, the abebraic rprsenair) of the plane that passed…

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Q: a) Draw an accurate graph of the portion of f(x,y) that is above the xy – plane. b) Describe the 2D…

A: We have to graph the function.

Q: acts about the base of a right prism and the height of the prism are given.Sketch each prism and…

A: Note: According to the guidelines only one question will be answered please upload other parts…

Q: The intersects Line Li: 0.5C1- x)= 2= 0.5z the plane defined by B(2,2っ7), C くりっ2) at point P- Find…

A: Given: The line L1: and the plane defined by the points

Q: 35. DISCOVER: Intersection of a Line and a Plane A line has parametric equations y = 3t 2= 5 - 1 x =…

A: Given :   We have given parametric equations of the line                 x = 2+t           y = 3t…

Q: det äLt)=cost ēit test(2-t-cost) ēga Show that the plane ď is plane curve, and defermine that curve…

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Q: ABC is a plane in three dimensions of equation (6 + 12)x− (4 +6)z = 20 + (6 + 2)y. Graph the plane…

A: Given, 3-dimensional equation is (6+12)x-(4+6)z=20+(6+2)y We can write it as…

Q: Quèstion 2 Given a sphere with center (8, 2, – 3) and radius 4. Find an equation of the intersection…

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Q: Pentagon ABCDE is rotated 90° counterclockwise about the origin to form pentagon A'B'C' D'E'. What…

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Q: Consider the surface area of the plane ax + by + cz + d = 0 completely contained in the first…

A: Given , If f and its first partial derivative are continuous on the closed region R in the xy-plane,…

Q: HOME WORK: find the distance from the point (1, 0,-1) to the plane -4x +y+z 4

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Q: urface S is parametrized by equations x = u + v, y = 3u², z = u – v; The point P (2, 3, 0) lies on S…

A: In this question, the concept of the derivative is applied to find out the equation of a tangent…

Q: Find the volume of water in a swimming pool with vertical ends and sides. The length measured at the…

A: Draw the swimming pool with vertical ends and side as shown below.

Q: Designing a gondola The designer of a 30-ft-diameter spherical hot air balloon wants to suspend the…

A: Given information:

Q: HOME WORK: find the distance from the point s(1.0.-1) to the plane -4x +y+z = 4

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Q: The Line whose eduation is (X + 2y +Z=!) > Cx -y + 2Z +7 =0) intersecks X Z plane. write equation of…

A: The line represented by the equation x+2y+z=1 and x-y+2z+7=0 intersects the XZ plane.

Q: 3. The equilateral triangular lamina A B C is placed perpendicular to the V. P. and having the…

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Q: In Exercises 35–44, describe the given set with a single equation or with a pair of equations.

A: Since you have posted multiple subparts, as per our policy we will answer first three subparts.…

Q: 2. Find a rectangular equation to represent the plane curve. If needed, state the appropriate…

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Q: Find the volume of water in a swimming pool with vertical ends and sides. The length measured at the…

A: Observe the following.

Q: uestion 11: The planes P and P2 are defined by the equations below. P: ar – 2y + 4z = 2 P2:r- y+ 2z…

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Q: 2. Given point P = (1,2,1) and Q(3,3,0) Find b) the coordinates of the point M, where line L meets…

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Q: The equation of the ine is [x,y,z] [-1,-1, 1] +s [1,0,1]++[0, 1,2], s, tEIR. find the intercept. of…

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Q: (1) y = 12 – x², y = x² – 6

A: Since you state area in rectangular coordinate I do first question of the above as per our company…

Q: Integrate ƒ(x, y) = 1/ (1 + x2 + y2 )2 over a. Triangular region The triangle with vertices (0, 0),…

A: Given Data The function is f(x,y)=1/(1+x²+y²)².   (a) The triangular vertices are (0,0), (1,0), and…

Q: 1. Find an equation for the plane consisting of all points that are equidistant from the points (1,…

A: We have to find the equation of Plane for given Condation.

Q: The Line whose edualion is (X + *y +Z=!) > (x -y +2Z+7 =0) intersecks the parametric Rind the X z…

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Q: where s, t E R. The plane contain the points P(1,-1,-4) and Q(2,1,-3). Moreover, contains the line I…

A: As you have mentioned I am answering number 4

Q: Parallelogram RSTV; also XY || VT 21 = LS First show that RSYX is a parallelogram. Given: Prove:…

A: Given: Parallelogra RSTV and XY¯∥VT¯. To prove: ∠1≅∠S Proof: Given diagram is: We know that…

Q: Ehe equation of a plane through the point (- 8,- 8, 3) and orthogonal to t) = - 8+ 8t E) = – 2+ 3t |…

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Q: 0lar coordinates to tind the volume: 2=6-R-y² and the paraboloid z=6-x-y² and 'ty² L4. 2. the plane…

A: For polar coordinates x^2+y^2 = r^2, dxdy = rdrdtheta x = rcostheta , y = rsintheta

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.