Find the moments and center of mass of the system of objects thathave masses 3, 4, and 8 at the points ( -1, 1 )  , ( 2, - 1 )  , and  ( 3, 2 )

Q: Find the volume of the parallelepiped determined by the vectors a = (5, 2, – 1), b = (0, 4, 1), č =…

A: We will find the volume of the parallelepiped by using the given vectors.

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: Find the centroid of masses of 3,5,7 units at (3,-2,3), (0,1,2) and (3,2,3) respectively

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Q: Find the volumes of the regions. The tetrahedron in the first octant bounded by the coordinate…

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Q: 2. Find the volume of the parallelepiped formed by vectors d (-1, 2, 1), 6 = (3, –2, – 1) and T =…

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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: Compute the volume of the parallelepiped dened by the vectors v1 = (1, 3, 1), v2 = (2, 1, -1) and…

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Q: Find the volume of the parallelepiped determined by the vectors = (1, 2, 3), b = (3, 0, 6) and c =…

A: This question is related to vectors, we will solve it by using the formula of volume of…

Q: Find the center of mass (in cm) of the particles with the given masses located at the given points…

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

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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 volume of the parallelepiped spanned by the vectors (1,-2, 1, -2), (0, 2, 1,1), (1,0,3,0),…

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Q: Find the volume of the parallelepiped with edges defined by the vectors u, v and w, where ü = (3,…

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Q: Find the volume of the parallelepiped spanned by the vectors below. u = [-3, –7,0] v = [5, –1, 7] w…

A: We can solve it by cross and dot product multiplications.

Q: Find the center of mass of  Y = x2/3    and. y = 4.

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Q: Find the volume of the parallelepiped determined by the vectors a, b, and c. а 3 (6, 2, -2), ь 3 (о,…

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Q: Compute the volume of the parallelepiped defined by the vectors v1 and v3 = (1,0, 1). (1,3, 1), v2 =…

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Q: 8. What is a center of mass? a centroid?

A: We have explain what is center of mass and a centroid

Q: What is a center of mass? a centroid?

A: To define centre of mass and centroid of an object.

Q: Find the volume of the parallelepiped determined by the vectors ā = (5, 4, – 1), b = (0, 1, 4), č =…

A: Given query is to find the volume of the parallelopiped.

Q: Find the centroid of a homogeneous half-ball of radius R.

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Q: 5- Find the volume of the box (parallelepiped) determined by the vectors 0 = (0,0,0), B = (1,1,2)…

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Q: Find the volume of the parallelepiped determined by the vectors a = (2, 3, – 1), 6 = (0, 2, 1), c=…

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Q: find a homogeneous linear system of two equations in three unknowns whose equation in three unknowns…

A: For the solution of the problem follow the next step.

Q: volume of the parallelepiped defined by the vectors v1 = (1, 3, 1), v2 = (2, 1, −1) and v3 = (1, 0,…

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Q: 9. Find the volume of the parallelepiped defined by the vectors. [8, – 3,4]v = [-2,9, 1] w = [0, –…

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Q: Find a homogeneous system whose solution space is spanned by the following sets of three vectors:…

A: This question is related to linear algebra.

Q: 2. Find the center of mass of the four particles having masses 2, 3, 3, and 4 kg and located at the…

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Q: Find the volume of the parallelepiped defined by the vectors 3 -3 -5 2 -3 Volume: %3D

A: Given:The given vectors are a=(3,-3,-3), b=0,-5,1,c=0,2,5To find:The volume of…

Q: Find the center of mass x of the point masses lying on the x-axis. = 5, m, = 4, m, = 8 8, X4 m, = 7,…

A: Given,

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: Scalar mutiple of z=(4,3,-2)

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Q: 5) Find the volume of the parallelepiped defined by vectors u = [1, -3, 6], v[-2, 5, 6] & w = [1, 2,…

A: Calculating the volume of parallelepiped

Q: Compute the volume of the parallelepiped defined by the vectors vị = (1,3, 1), v2 = (2, 1, – 1) and…

A: Given that three sides of the parallelepiped are: v1 = (1,3,1) , v2=(2,1,-1) , v3=(1,0,1) So the…

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

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Q: Compute the volume of the parallelepiped defined by the vectors vi and v3 = (1,0, 1). (1, 3, 1), v½…

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Q: The center of mass of a composite body: O is the same as the center of gravity of the composite…

A: To find- The center of mass of a composite body: Is the same as the center of gravity of the…

Q: Use Lagrange multipliers to find a vector in 3-space whose length is 7/3 and whose components have…

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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: Find the volume of the parallelepiped determined by the vectors a (3, 4, 1), b = (0, 2, 4), = (2, 4,…

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Q: 4

A: We have to find the equation of plane according to the given information

Q: Find the center of mass of the particles with the given masses located at the given points. 18) 11…

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Q: Compute the volume of the parallelepiped defined by the vectors v1 = (1,3, 1), v½ = (2, 1, –1) and…

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Q: Find the volume of the parallelepiped determined by vectors , and

A: Find the volume of the parallelepiped determined by vectors <3,1,4>, <2,0,2> and…

Q: Compute the volume of the parallelepiped defined by the vectors v = (1,3,1), v2 = (2, 1, -1) and v3…

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Q: Find the center of mass of the three particles having masses of 1, 2, and 3 kg located at the points…

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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: Locate the coordinates of the centroid/center of gravity X

A: concept: First we have to find equation of given Circle of radius r. With the help of given Circle…

Q: Find the center of mass of the given system of point masses.   Please see attached image

A: Center of…