A fish tank in an avant-garde restaurant is in the shape of a parallelepiped with a rectangular base that is 280 cm long and 120 cm wide. The front and back faces are vertical, but the left and right faces are slanted at 30° from the vertical and measure 120 cm by 150 cm. V 30° (a) Let u, v, and w be the three vectors shown in the figure. Find u · (v x w). [Hint: Recall that u · v = Ju||v| cos(0) and Ju x v = Ju||v| sin(0).] (b) What is the capacity of the tank in liters? [Note: 1 L = 1000 cm3.] (Round your answer to the nearest liter.)
A fish tank in an avant-garde restaurant is in the shape of a parallelepiped with a rectangular base that is 280 cm long and 120 cm wide. The front and back faces are vertical, but the left and right faces are slanted at 30° from the vertical and measure 120 cm by 150 cm. V 30° (a) Let u, v, and w be the three vectors shown in the figure. Find u · (v x w). [Hint: Recall that u · v = Ju||v| cos(0) and Ju x v = Ju||v| sin(0).] (b) What is the capacity of the tank in liters? [Note: 1 L = 1000 cm3.] (Round your answer to the nearest liter.)
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.3: Lines And Planes
Problem 31EQ
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![A fish tank in an avant-garde restaurant is in the shape of a parallelepiped with a rectangular base that is 280 cm long and 120 cm wide. The front and back faces are vertical, but the left and right
faces are slanted at 30° from the vertical and measure 120 cm by 150 cm.
30°
W
(a) Let u, v, and w be the three vectors shown in the figure. Find u · (v x w). [Hint: Recall that u · v = |u||v| cos(0) and |u x v|
|u||v| sin(0).]
(b) What is the capacity of the tank in liters? [Note: 1L = 1000 cm³.] (Round your answer to the nearest liter.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4aaaa656-9ce8-4460-b0b3-3ffbf36b53a7%2Fccec4885-c3e3-45d6-8d54-b8c6a69ece1c%2F6981vnq_processed.png&w=3840&q=75)
Transcribed Image Text:A fish tank in an avant-garde restaurant is in the shape of a parallelepiped with a rectangular base that is 280 cm long and 120 cm wide. The front and back faces are vertical, but the left and right
faces are slanted at 30° from the vertical and measure 120 cm by 150 cm.
30°
W
(a) Let u, v, and w be the three vectors shown in the figure. Find u · (v x w). [Hint: Recall that u · v = |u||v| cos(0) and |u x v|
|u||v| sin(0).]
(b) What is the capacity of the tank in liters? [Note: 1L = 1000 cm³.] (Round your answer to the nearest liter.)
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