Let Q be the cube with vertices {(1, 1, 1), (1, 1, −1), (1, −1, 1), (1, −1, −1), (−1, 1, 1), (−1, 1, −1), (−1, −1, 1), (−1, −1, −1)} . Write Q in cylindrical coordinates.

Q: Find the scalar equation of the plane that contains these points: A (1, 13, 2), B (-2, -6, 5) and C…

A: In this question, we want to find the scalar equation of a plane Passing through given three points.

Q: Find a parametric representation of the line through the points P(1,-1,2) and Q(3,1,8).

A: The parametric equation of line through the points x1,y1,z1 and x2,y2,z2 is given by  x=x1+tx2,…

Q: Find the matrix A of the quadratic form associated with the equation. 7x2 + 7y2 + 7z2 + 6xy + 6xz +…

A: We will find corresponding matrix and then its eigen values to determine final equation eliminating…

Q: On a plane equipped with a polar coordinate system, what is the area of ​​the triangle with vertices…

A: In polar coordinate system x=rcosθy=rsinθ

Q: Find the scalar equation of the plane that contains (1,1,1), (3,-1,5), and (4,2,-2). -2x1 + 9x2 + x3…

A: Equation of the plane, passing through three points

Q: Consider a point in Cartesian coordinates given by (-2, 2v3, 4). (a) Find the corresponding…

A: Given,

Q: Find the centroid (ã, §) of the triangle with vertices at (0, 0), (2, 0), and (0, 8). || 18

A: Recall: Centroid of a Triangle with vertices are (x1,y1) , (x2,y2) and (x3,y3) is…

Q: Find the centroid (ĩ, g) of the triangle with vertices at (0, 0), (10, 0), and (0, 9).

A:

Q: Find the scalar equation of the plane that contain the line 7 = [2,1,7] + t[0, 1, 0], t e R and is…

A: Here we will find out the required plane.

Q: Find the coordinates of the centroid of APQR with vertices P(-2,5) , Q(4,1) , and R(-2,- 3). The…

A: Explanation of the answer is as follows

Q: Find a parametric representation of the line through the points P(4,1,2) and Q(3,5,7)

A:

Q: Find a scalar equation of the plane that contains the points (−1, −3, 1), (1, 0, 3), and (2, 7, 0).

A: We are going to solve

Q: Identify and sketch the solid figure that could be formed by the net.

A: 4. To identify the solid figure formed by the netof squares

Q: For a plane with a normal of n = [1, 2, - 9]   and containing a point P (3, -4, 0), write the…

A:

Q: 8. Find a parametric representation of the line through the point P(1,0,4) and perpendicular to the…

A:

Q: Find the image of the point A(-2, 4, 5) under a rotation of 60 degrees In the plane x = 2 about the…

A: We need to find image of given point.

Q: Prove that the centroid of a parallelogram is the point of intersection of the diagonals of the…

A: The vertices of the parallelogram are (0, 0), (0, a), (b, c), and (b, a + c)

Q: Find an equation for the sphere with center at (-7,8,0) and radius = 9 O x2 + y? O x2 + y2 + z- -…

A: We have to find

Q: Convert the point (x, y, z) = (2,2v3, 4) to spherical %3D coordinates (p, 0, 4).

A:

Q: Let P be the point in 3-space with rectangular coordinates (√2, -√2, 2√3). (a) Cylindrical…

A:

Q: Find a parametric representation of the solution set of the linear equation.−3x + 4y − 2z = 1

A:

Q: Find the rectangular coordinates of the point, whose cylindrical coordinates are given. (a) (4, n/4,…

A:

Q: Find Vector, Parametric and Scalar equations for the line that passes through t -2,11) and (6,1).

A: Given: - The line that passes through the points -2,11and 6,1. To find: - The parametric equations…

Q: Express the following points in cylindrical and spherical coordinates: (а) Р(1, — 4, — 3) | (b) Q(3,…

A:

Q: Let P be the point (4, 1/3, 5) in cylindrical coordinates. Find the x-coordinate of P in Cartesian…

A: Formula: For a point P in three-dimensional space represented with cylindrical coordinates r, θ, z,…

Q: Write the equations in cylindrical coordinates. (a) 3x² – 6x + 3y2 + z² = 5 z = 7x2 – 7y2

A:

Q: Find the symmetric equations of the L that is parallel to the two planes x+y-z= 2 and z + 3y+ z =…

A:

Q: Find the matrix A of the quadratic form associated with the equation. 3x2 + 3y2 + 3z2 + 4xy + 4xz +…

A:

Q: Give a parametric representation for the cylinder x^2+z^2=121

A:

Q: Find a parametric representation for the lower half of the ellipsoid 5x² + 4y2 + z² = 1.

A:

Q: Find the center C and the radius a for the spheres 3x2 + 3y2 + 3z2 + 2y - 2z = 9

A: Given: The equation of sphere as 3x2+3y2+3z2+2y-2z=9, To find: The center C and radius a for the…

Q: Find the canonical or standard equation of the sphere, if it exists. 2x² +2y² + 2z² – 4x+12y–16z+6=0…

A: To write the canonical or standard equation of the below sphere. 2x2+2y2+2z2−4x+12y−16z+6=0

Q: Which of the following is the cylindrical coordinates of (-1, 3, -2)? O a. (2, 플, 2) O b. (4, 품,-2)…

A:

Q: Which of the following is the cylindrical coordinates of (-1, –/3,2)? O a. (4, 품, 2) O b. (2, 플, 2)…

A:

Q: 1. Find the three cube roots of z =-j and sketch the result in a single Argand plane. (express…

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Q: Find an equation in spherical coordinates whose graph is the parapoloid Z=(X^2)+(Y^2)

A:

Q: Find the matrix A of the quadratic form associated with the equation. 6x² + 6y2 + 6z? + 8xy + 8xz +…

A: Given 6x2+6y2+6z2+8xy+8xz+8yz-1=0

Q: find the centroids of the triangleswhose vertices appear . Assume a, b > 0. (0, 0), (1, 0), (0,…

A:

Q: What kind of conic section is given by the quadratic form ? -11x,? + 84x,x2 + 24x2? = 156 Transform…

A: Given quadratic form is-11x12+84x1x2+24x22=156The above conic is determined and transformed to…

Q: Find the centroid of the triangle formed by joining the points A (3, 2), B (-1, 4), and C (5, -3).…

A: Explained below

Q: Convert the Cartesian equation Z z = 6-√√36-x² - y² into spherical coordinates.

A:

Q: 8. If the vertices of a triangle are A(8, 5), B(-1, 8) and C(2, -1) where would the centroid (Center…

A: Consider the vertices of a triangle is (x, y). The vertices of a triangle are: A(8, 5), B(-1, 8) and…

Q: a)Find the equation of the plane in 3- dimensional space passing through the points P = (1, 2, 1), Q…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find a parametric representation = z(t) for the upper half of = Z Iz – 4+ 2i| = 3.

A: Given to represent parametrically z=zt for the upper half of  z-4+2i=3 Let z=x+iy Then the equation…

Q: 4) Find equations for the planes: a. The plane through P(0,2,-1) normal to n = 3i-2j-k

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Q: Determine the rectangular form of z (1 + i)!-i

A:

Q: 6.) Consider the points P(-1,2,5), Q(2, –3, 0) and (i) Write an equation of the plane containing t

A: Equation of plane: We know that, the equation of plane that passes through point (x, y, z) is given…

Q: Find an equation for the sphere with the given center and radius. Center (0, -4, -1), radius 9 O x2…

A: In this question we have to find the equation of sphere.

Q: Find the centroid (ã, g) of the triangle with vertices at (0, 0), (5, 0), and (0, 9). y=

A: In the question it is asked to find centroid of the triangle with coordinates (0,0), (5,0) and…