Volume In Exercises 35 and 36, use t triple scalar product to find the volume of t parallelepiped having adjacent edges u, v, and w.
Want to see the full answer?
Check out a sample textbook solutionChapter 11 Solutions
Calculus (MindTap Course List)
- A closed rectangular box with faces parallel to the coordinate planes has one bottom corner at the origin and the opposite top corner in the first octant on the plane 6x + 2y +z = 1. What is the maximum volume of such a box? volume = Submit answerarrow_forwardConsider the parallelepiped with adjacent edges Find the volume. V = i 248 u = 5i + 2j + k v=i+j+ 7k w = i + 9j + 5k eTextbook and Media Hint The volume V of the parallelepiped that has the vectors u= (u₁, U₂, U3), V = (V1, V2, V3), (W₁, W2, W3) as adjacent and w= edges is V = Assistance Used | u . (V x W)|arrow_forwardplease solve the centroidal Ix, centroidal Iy, Ix and Iyarrow_forward
- Opic: Area of a plane Regionarrow_forwardUse the triple scalar product to find the volume of the parallelepiped having adjacent edges u = 3i + j, v = 3j + k, and w = -j+ 3k. Need Help? Read Itarrow_forwardEdit Consider the points A(3, –2,3), B(4, –4, 1), C(-2, –3, 1), and D(5, 3, –4). - (a) Find the volume of the parallelepiped that has the vectors AB, AC, and AD as adjacent edges. NÓTE: Enter the exact answer. Volume =|141 (b) Find the distance from D to the plane containing A, B, and C. NOTE: Enter the exact answer. Distance = 11arrow_forward
- View Policies Current Attempt in Progress Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v and w is u (v × w)| to determine the volume of the tetrahedron with vertices P(-4,7,0), Q(2, 1, –3), R(1,0, 1) and S(3,-2, 3). NOTE: Enter the eract answer. for Later Attempts: 0 of 3 nultiple attemnts will imnnarrow_forward43. Volume of a Parallelepiped Find the volume of the parallel- epiped determined by the vectors u = 2i - j, v = 2j + k, and w = 31 +j - k.arrow_forwardUse the triple scalar product to find the volume of the parallelepiped having adjacent edges u, v, and w. = (1, 3, 1) (0, 6, 6) (-4, 0, -4) U = y = W = z 6 4 yarrow_forward
- Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u, v, and w. u = (1, 3, 1) v = (0, 6, 6) w = (-4, 0, -4) CT N 6arrow_forward(c) Consider the parallelepiped with sides: u=(5,-2,1), v=(3,2, 4), and w=(-6,1,1). V (i) Find the volume of the parallelepiped.arrow_forwardMaximum curl Let F = ⟨z, x, -y⟩.a. What is the scalar component of curl F in the direction of n = ⟨1, 0, 0⟩?b. What is the scalar component of curl F in the direction ofn = ⟨0, -1/√2, 1/√2⟩?c. In the direction of what unit vector n is the scalar componentof curl F a maximum?arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning