   Chapter 12.4, Problem 33E

Chapter
Section
Textbook Problem

# Find the volume of the parallelepiped determined by the vectors a, b. and c.33. a = ⟨1, 2, 3), b = ⟨−1, 1, 2⟩, c= ⟨2, 1, 4⟩

To determine

To find: The volume of the parallelepiped determined by the vectors a,b and c .

Explanation

Given:

a=1,2,3,b=1,1,2 and c=2,1,4 .

Formula:

Write the expression for cross product between a and b vectors.

a×b=|ijka1a2a3b1b2b3| (1)

Write the expression for dot product between a and b vectors.

ab=a1b1+a2b2+a3b3 (2)

Write the expression to find volume of the parallelepiped (V) .

V=|a(b×c)| (3)

Modify equation (1).

b×c=|ijkb1b2b3c1c2c3|

Substitute 1 for b1 , 1 for b2 , 2 for b3 , 2 for c1 , 1 for c2 and 4 for c3 ,

b×c=|ijk112214|=|1214|

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