53. Medians of a triangle Suppose that A, B, and C are the corner points of the thin triangular plate of constant density shown here. a. Find the vector from C to the midpoint M of side AB. b. Find the vector from C to the point that lies two-thirds of the way from C to M on the median CM. c. Find the coordinates of the point in which the medians of AABC intersect. According to Exercise 27, Section 6.6, this point is the plate's center of mass. (See the figure.) C(1, 1, 3) c.m. •B(1, 3, 0) х A(4, 2, 0)

Q: Suppose that A, B, and C are the corner points of the thin triangular plate of constant density…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v and w is…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v and w is…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w…

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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: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v and w is…

A: The given expression for the volume of a tetrahedron is; V=16u·v×w And The vertices are P-6,7,0,…

Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w…

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Q: 50. Find the vector from the origin to the point of intersection of the medians of the triangle…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w…

A: This question is based on finding the adjacent edges of tetrahedron and dot and cross product use.

Q: 18!- Use the vectors to find the area of the triangle with vertex A(1,0,1), B(0,2,3) and C(2,1,0).

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

Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v and w is…

A: To find the volume of the tetrahedron whose vertices P , Q , R and S are given .

Q: Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v and w is…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v and w is…

A: Given: The expression for the volume of tetrahedron is: V=16u·v×w And The vertices P-2,5,0, Q2,1,-3,…

Q: Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v and w is…

A: Volume of a tetrahedron with adjacent edges given by the vectors u,v,w is given by, V= |u.(v×w)|/6

Q: Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v and w is…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v and w is…

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Q: Find the volume of the parallelepiped defined by the vectors й%3 (3, —1,4), ѣ —D (2, 1, —2) and й %3…

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Q: What three points are on the line L: vector r= (2,-5) + s(2,1), sER

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Q: )ca) if vector as 6=2ナリーk Calculate axb and bxa. (b) Find The area of the paralletogrmais bounded by…

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Q: (a) Find the vector projection of a onto b , that is, find proj, a . (b) Find a vector in the…

A: We can solve the problem problem using concept of vector.

Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v and w is…

A: Given that the volume of a tetrahedron with adjacent sides u, v and w is given by, 16u·v×w. The…

Q: Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v and w is…

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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,…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v and w is…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w…

A: Finding the volume of tetrahedron

Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w…

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Q: Suppose u = (1,0), v = ( ), Dulw(a, b)) = 3, and D,((a, b)) = v2. Please find Vy(a, b). What is the…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w…

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Q: Suppose that A, B, and C are thecorner points of the thin triangular plate of constant density…

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Q: Find volume of the parallelepiped determined by the vectors a = (8, 1,0), E b = : (1,4, 1), and c =…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v and w is…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w…

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Q: 18. Calculate the volume of the of the parallelepiped spanned by the following vectors. Interpret…

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Q: 3. Show (using the concept of vectors) that the area of the triangular region with vectors u 1 and v…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w…

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Q: Let A=(3,3,−4), B=(0,−2,−2), and P=(k,k,k). The vector from A to B is perpendicular to the vector…

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Q: ve : 9) A líne that passes througn the points MCO,1,4) and N(1,4,5). Find a vector eguation of the…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w…

A: Solution is given below:

Q: A force is given by a vector F = (1,2, 3) and moves a particle from the point P(2, 1, 0) to the…

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Q: Suppose that A, B, and C are thecorner points of the thin triangular plate of constant density…

A: To find the vector C to the midpoint of the side AB.