   Chapter 12.4, Problem 34E

Chapter
Section
Textbook Problem

# Find the volume of the parallelepiped determined by the vectors a, b. and c.34. a = i + j , b = j + k, c = i + j + k

To determine

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

Explanation

Given:

a=i+j,b=j+k and c=i+j+k .

Formula:

Consider two three-dimensional vectors such as a=a1,a2,a3 and b=b1,b2,b3 .

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 0 for b1 , 1 for b2 , 1 for b3 , 1 for c1 , 1 for c2 and 1 for c3 ,

b×c=|ijk011111|=

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