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.
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Calculus
- Cal 3 HW 11.4 Q8arrow_forward? Question Use the new command from Example 3 above to find the volume of the parallelepiped formed by vectors i = (1, 0, 0), i = (1,1, 0), and u = (0, 1, 1). Volume • Hintarrow_forwardA blade on an industrial fan has the configuration of a semicircle attached to a trapezoid (see figure). Find the centroid of the bladearrow_forward
- Using the fact that the centroid of a triangle lies at the intersection of the triangle's medians, which is the point that lies one-third of the way from each side toward the opposite vertex, find the centroid of the triangle whose vertices are (0,0), (a,0), and (0,b). Assume a > 0 and b>0. The centroid of the triangle is (x,y), where x = and y =arrow_forwardExercise: Let u=[3,−2,1]�=[3,−2,1], v=[1,1,1]�=[1,1,1] and w=[2,−2,0]�=[2,−2,0]. The area of the parallelogram formed by u� and v� is A=√�=Answer 1 Question 14. The volume of the parallelepiped formed by u,v�,� and w� is V=�=Answer 2 Question 14. Given that the volume of a parallelepiped is the area of its base times its height, the height of the parallelepiped formed by u,v�,� and w� when its base is viewed as the parallelogram formed by u� and v� is h=ℎ=Answer 3 Question 14/√/Answer 4 Question 14. The parallelepiped formed by u� and v� and ku×v��×� will have the same volume as the parallelepiped formed by u,v�,� and w� if k=±1/�=±1/x. what is x ?arrow_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_forward
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- Drinking juice A glass has circular cross sections that taper (linearly) from a radius of 5 cm at the top of the glass to a radius of 4 cm at the bottom. The glass is 15 cm high and full of orange juice. How much work is required to drink all the juice through a straw if your mouth is 5 cm above the top of the glass? Assume the density of orange juice equals the density of water.arrow_forwardEXAMPLE 6 Find the volume of the box (parallelepiped) determined by u = i + 2j – k, v = -2i + 3k, and w = 7j – 4k.arrow_forwardSolve using euclid geometry. Include helpful diagrams.arrow_forward
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