Find the centroid of the triangle whose vertices are  O(0,0) , A(4,0) and B(0,6)

Q: Find a linear mapping G that maps [0, 1]×[0, 1] to the parallelogram in the xy-plane spanned by the…

A: A linear mapping G that maps [0, 1]×[0, 1] to the parallelogram in the xy-plane spanned by the…

Q: Compute the new position of the square [A(19,19), B(29,19), C(29,29), D(19,29)] after its rotation…

A: ABCD is a square , we need to rotate it clockwise along with centroid.

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: Determine the volume of the box whose sides are the vectors (1, -2, 1), (2, 3, -2), (-1, 3, -2)

A: use determinant method to findout the volume.

Q: 2. The plane containing the point (-8, 3, 7) and parallel to the plane given by 4x+8y-2z=45.

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Q: Find the volume of the parallelepiped spanned by the vectors a =(-2,3, 1), b = (0, 4, 0), and c =…

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

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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 the centroid (x¯,y¯) of the triangle with vertices at (0,0), (6,0), and (0,1).

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Q: Find all vectors in R' that are perpendicular to both [1,0, 1, 0] and [1,2,0, 1] and then find a…

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Q: 12. Find the volume of the parallelepiped spanned by the vectors (1, 1, 2), (2,2, 1), and (0, –4,…

A: The given vectors 1,1,2, 2,2,1, 0,-4,0

Q: Find the dimensions of the rectangular box of maximum volume with faces parallel to the coordinate…

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Q: ear equation of the plane through the nts (6, 3, 2) and (4, −1, 1).

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Q: Find the least squares approximating parabola for the given points. (-2, 0), (–1, –11), (0, –10),…

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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: Find the coordinates of the centroid of the triangles whose vertices are: a. (5.7), (1, -3), (-5.1);…

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Q: Do the vectors (1, 0, 0), (0, 1, 0), and (2, 3, 0) lie on the same plane? Briefly explain how you…

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Q: Find the projection of ū = (2, -3, 1) onto v = = (-3, 0, 1) %3D 3 0, А. B. (3.0. -1) В.

A: u→ =2, -3, 1v→ =-3, 0, 1v→ =(-3)2+02 +12       =9+1|v→| =10    u→  · v→ =2, -3, 1·-3, 0, 1u→  · v→ =…

Q: The vertices of AJKL are J(-3, 4), K(3, 0), and L(-5, -4). The equation of the median JLis y = 0.…

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Q: 7. Find the centroid of a triangle whose vertices are (2, 3), (-4, 6) and (2, -6). В. (0, -1) A. (0,…

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Q: Find the centroid of the triangle whose vertices are at points (3,4). (6.-9) and (6,-2). asap pls

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Q: 3. Calculate the centroid of the given illustration below. y-axis 7.5ft- 4ft 2ft 5ft- х-ахis 2ft

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Q: y -6- 4- 3- 2- 1- -3 2 -1 0 12 3 4 5 6 -1- -2- R -3- your work on question 10, classify this…

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Q: Use cross products to find the area of the triangle in the xy-plane defined by (1,2), (3,4), and…

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Q: Defined byT (x, y, z) = (y+2z, –2x+y+2z, –3x– y+52), is diagonalizable.

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Q: Find the scalar equation for the plane passing through the points P-(-1. 5.-1. P=(-1, 6, 5), and…

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Q: If (-2, 3), (4, -3) and (4, 5) are the mid-points of the sides of a triangle, find the coordinates…

A: On solving this we will get:-

Q: A point moves so that sum of the squares of its distances from the vertices of a triangle is always…

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Q: Find y': %3D Oy =- Oy=--

A: A detailed solution is given below

Q: Z is a complex variable, z=x+iy

A: The z is complex variable with z = x + i y , and the given vertices are (0,0),(1,0),(1,1) and (0,1).

Q: DEFINE Centroids

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Q: 2) Find the vector from the origin to the center of the sphere 2x2 + 2y2 + 2z2 + 4x – 4z = 0.

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Q: 5. What are the coordinates of the centroid of triangle FGH: F(6,-1), G(12,4), H(15,-2)?

A: follow next step

Q: Calculate the dot product of x = (3, -2, 0, 3) E R and y = (1, 2, 3, 4) ER4.

A: The dot product of two vectors x=(a1,a2,a3,a4)  and  y=(b1,b2,b3,b4)in 4th-dimensional space is: x.y…

Q: Find the centroid of the triangle if the vertices are  (0,0) , (4,0) and (0,6)

A: Given points are         0,0,4,0,&0,6      And centriod G ?      centriod G= x1+x2+x33…

Q: Prove that the centroid of any triangle is located at the pointof intersection of the medians.…

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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: Find the least squares approximating parabola for the given points. (1, 4), (2, -5), (3, 6), (4, 9)…

A: Solve

Q: Find the centroid (, ) of the triangle with vertices at (0, 0), (10, 0), and (0, 2). 19 120 y=

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Q: 2) Find the vector from the origin to the center of the sphere 2x² + 2y² + 2z2 + 4x - 4z = 0.

A: The equation of the sphere is, 2x² + 2y² + 2z² + 4x - 4z = 0 So, x² + y² + z² + 2x - 2z = 0 So, (x²…

Q: Determine the scalar equation of the plane that passes through (5, -5, 5) and is perpendicular to…

A: Here we will find the required equation of the plane,

Q: The centroid of a triangle lies at the intersection of the triangle's medians, because it lies…

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Q: 2) Find the vector from the origin to the center of the sphere 2x2 + 2y² + 2z2 + 4x – 4z = 0. |

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Q: Find the scalar product of x and y x =(-1, 0, 2) and y =(-7, 7, 3)

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Q: Calculate the dot product of u = (-5,–2,7,–3) and v (-3, 1,5, 8). u • V =

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Q: Find the center of mass of the triangle with vertices (0, 0), (2, 0) and (2, 6).

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Q: Find the centroid when revolved in y-axis: y³ = x² ; y = 4.

A: As per the question we are given a solid of revolution obtained by rotating the area between y3 = x2…

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…

Q: Find an equation of the plane passing through the points.(0, −1, 0), (1, 1, 0), (2, 1, 2)

A: we have to find an equation of the plane passing through the points (0,-1,0), (1,1,0), (2,1,2)