Determine whether or not the points A(1,3,−2), B(3,4,1), C(2,0,−2), and D(4,8,4) are coplanar. If not, find the volume of the pyramid with these four points as its vertices, given that its volume is one-sixth that of the parallelepiped spanned by AB, AC, and AD

Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS. P(2, 0, –1), Q(4, 1, 0),…

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Q: 9. DABCD is a convex quadrilateral. Let P, Q, R, S be centers of the squares drawn (externally to…

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Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS where P(-2,1,0) Q(2, 3, 2)…

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Q: Show that the volume V of a parallelepiped having u, v, and w as adjacent edges is V = ∣u ∙ (v ×…

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Q: Let u = i−5k, v = 2i−4j + k,and w = 3i−2j + 5k. (a) u · (v × w) = ______. (b) The volume of the…

A: Given :           u = i - 5k , v = 2i - 4j + k, w = 3i - 2j + 5k

Q: Find T, N and k for the spacecurves:

A: We have to find Unit Tangent Vector T,  Unit Normal Vector N and Curvature K for given space curve…

Q: a =i +j +2k,b =i+k,č = j +k.

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Q: Find the surface area of the tetrahedron bounded by the coordinate planes and the plane 8x + 12y +…

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Q: Find the volume of parallelepiped if A = ai + aj, B = cj + ck and C = bi + bk

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Q: Find the volume of the parallelepiped having adjacent edges u, v, and w; for u = (1,-1,0), v =…

A: Given u=1,-1,0, v=0,2,2 and w=1,3,1

Q: Find the volume of the parallelepiped (box) determined by u, v, and w while: u = 10i + 20j + 50k, v…

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Q: The volume of the pyramid formed in the first octant by the plane 6x + 10y + 5z-30 = 0 is: О 45 О зо…

A: We can solve as follows

Q: Prove that if ABCD is the given rectangle, AE is the diameter of a semicircle, and BFGH is a square,…

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Q: 日-1- Find the volume of the parallelepiped determined by w = |0,v = 1, and u =|1

A: The Volume of parallelepiped formed between three vectors A→,B→ and  C→ is given by the scalar…

Q: Find the volumes of the solids generated by revolving the triangle with vertices (2,2), (2,7), and…

A: Given data: *The vertices of the triangle is (2,2), (2,7) and (4,7) From the coordinates of the…

Q: Find the volumes of the regions. The wedge cut from the cylinder x2 + y2 = 1 by the planes z = -y…

A: Given Data The equation of a cylinder is x2+y2=1. z=-yz=0   Determine the interval of x and y,…

Q: Prove that the midsegment of a trapezoid is parallel to the bases and its length is the average of…

A: To prove that the mid-segment of a trapezoid is parallel to its base, first consider a trapezoid…

Q: Find the volume of a parallelepiped whose edges are ä = 7i+5j-k, 6-j+4k and e= 4i-3j+6k %3D

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Q: Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u = 4i…

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Q: Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u, v,…

A: Given, u=i+jv=j+kw=i+k

Q: Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u, v,…

A: Find the volume of parallelepiped

Q: E and F are points of the sides AD, BC of a quadrilateral ABCD such that AE = kED and BF = kFC. If…

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Q: Find the volume of the parallelepiped (box) determined by u, v, and w. u V i+ 3j 4i - j+4k 2i + 4k

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Q: Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u, v,…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS where P(-2, 1, 0) Q(2, 3,…

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Q: Find the volume of the parallelepiped with adjacent edges t = 3j – 4j – 6k, u = 3i – 7j – 7k and v =…

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Q: Use a scalar triple product to find the volume of the parallelepiped that has u, v, and w as…

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Q: Find the volume of a parallelepiped if four of its eight vertices are P(0,0,0), Q(3, 4, 0), R(0, –3,…

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Q: Find the volume of the parallelepiped spanned by u = (1, 0, 4), v = (1, 2, 1) and w = (-4, 2, 9) in…

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Q: Find the area of the parallelogram spanned by v = (1, 1, 1) and w = (0, 0, 2).

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Q: Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u, v,…

A: We have to find

Q: Find the volumes of thetetrahedra whose vertices are A(0, 0, 0), B(2, 0, 0), C(0, 3, 0), D(0, 0, 4)

A: Consider the following vertices: A0,0,0, B2,0,0, C0,3,0, D0,0,4…

Q: XydA, D is the triangular region with Vertices (0,0), Cu,0], and Cor) SketchD onthe XY planel

A: 8/3

Q: Find the volume of the parallelepiped shown having    u = 3i − 5j + k ,            v = 2j − 2k and w…

A: Givenu=3i−5j+kv=2j−2kw=3i+j+k

Q: Find the volume of the box (parallelepiped) that is determined by u = i + 2j - k, v = -2i + 3k, and…

A: Solution:-  The given vector is  u→=i+2j-kv→=-2i+0j+3kw→=0i+7j-4k

Q: Assume that a = b + d. a. Show that the trapezoid is isosceles. b. Prove that its diagonals are…

A: Given  Here assume that a = b + d.

Q: Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u, v,…

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Q: Find the volume of the parallelepiped with adjacent edges t = 3j – 4j – 6k, u = 3i – 7j – 7k and v =…

A: t =3j–4j–6k, u=3i–7j–7k and v=5i+ j+3kTo find the volume of the parallelepiped

Q: Find the volumes of the solids generated by revolving the triangle with vertices (2,2), (2,7), and…

A: Using washer method

Q: Find the volumes of thetetrahedra whose vertices are A(0, 0, 0), B(1, 0, 2), C(0, 2, 1), D(3, 4, 0)

A: The vertices of the tetrahedra are A(0, 0, 0), B(1, 0, 2), C(0, 2, 1), D(3, 4, 0). The volume of the…

Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS where P(-2,1,0) Q(2,3, 2)…

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Q: Find the points on the cone z? = x² + y² that are closest to the point (4,2,0).

A: Given :       z2 = x2 + y2  at (4 , 2 , 0)   Minimize the distance function is   f(x ,y ,z) =  (x -…

Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS where P(-2, 1, 0) 2(2, 3,…

A: Follow next step

Q: Given A ABC with points A (-1,2) B(4,-3) and C (0,0) dilated about a center at the origin by a scale…

A: Topic:- Geometry

Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS where P(-2, 1,0) Q(2, 3, 2)…

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Q: (b) Prove the volume of a parallelepiped with a vertex at the origin and edges ü,v, and w is given…

A: In the question we have to prove the formula.

Q: Find the volume of the parallelepiped with adjacent edges PQ, PR and PS given the  points P = (−2,…

A: We have to find

Q: Let the points B, C be perpendicular to the bases O and A (13,0), respectively, on the line 5x-12y +…

A: Given equation of line: 5x-12y+65=0 Coordinates of point A: (13,0)  Coordinates of point O: (0,0)

Q: The volume of the parallelepiped that has u, v, was adjacent edges u = 3i +j+ 2k , v = 4i + 5j + k,…

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Q: 1 %3D 12 27

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