Find the volume of the parallelepiped defined by the vectors lessthan 2, 0, 0
b. Find the volume of the parallelepiped spanned by the vectors (t, 0,0), (1,2,-4), (0, t,-1). For what values of t will there be a zero volume? What can you say about the three vectors when the volume is zero? Using a 3D graphing program, include two graphs of the three vector, one where the volume is not zero and one where the volume is zero. (9pts) b. Find the volume of the parallelepiped spanned by the vectors (t, 0,0),...
Find the volume of the parallelepiped spanned by the vectors u=〈3,−2,2〉, v=〈1,0,1〉, and w=〈−2,1,−5〉. Write the exact answer. Do not round.
Find the volume of the parallelepiped with one vertex at (-4,-2,-1), and adjacent vertices at (-9,0,-7), (-1 ,-6,-1), and (0,-2,3) Volume 120 Find the volume of the parallelepiped with one vertex at (-4,-2,-1), and adjacent vertices at (-9,0,-7), (-1 ,-6,-1), and (0,-2,3) Volume 120
8. A parallelepiped is formed by the vectors a,1,0, b 0,1, 1 and c1,1 e the volume of the parallelepiped. etermin 9. Show that the four points A(1,3, 2), B(3,-1,6), C(5, 2,0) and D(3,6,-4) are copla- nar
(b) Find the area of the triangle PQR. Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS. P(−2, 1, 0), Q(3, 5, 3), R(1, 4, −1), S(3, 6, 2) 9. +5/10 points | Previous Answers SCalcET8 12.4.029 Consider the points below. (a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R. 〈0.16,-8) (b) Find the area of the triangle PQR. Need Help? Read It Watch It Talk to a Tutor...
IX. (5%) Find the volume of the parallelepiped with a vertex in the origin and the adjacent vertices in the points A(-2,2,0), B(0,4,-2), C(3,6,1)
Can you help me solve this problem? A parallelepiped is a prism whose faces are all parallelograms. Let A, B, and C be the vectors that define the parallelepiped shown in the figure. The volume V of a parallelepiped is given by the formula. V- l(AxB).cl Find the volume of the parallelepiped with edges A-5i-7j+4k, B--i +4j+k, and C- 7i- 7j+ 4k. The volume of the parallelepiped is cubic units (Simplify your answer.)
Determine the volume of the parallelepiped with one vertex at the origin and the three vertices adjacent to it at (0, 1, 0), (4, 1, -3), and (4, -3, -2). Volume = 0
Problem 2 (1.1.5, 4 points): Find the rectangular parallelepiped of unit volume that has the minimum surface area. Hint: By eliminating one of the dimensions, show that the problem is equivalent to the minimization over > 0 and y > 0 of f(x,y) =xy +-+- Show that the sets {(x,y) I f(x,y) x > 0, y > 0} are compact for all scalars γ.
I. a. (10) Find the volume of an axisymmetric ‘gum drop, defined by 0< zく1- I. a. (10) Find the volume of an axisymmetric ‘gum drop, defined by 0