   Chapter 12.4, Problem 36E

Chapter
Section
Textbook Problem

# Find the volume of the parallelepiped with adjacent edges PQ, PR. and PS.36. P(3, 0, 1), Q(−1, 2, 5), R(5, 1, −1), S(0, 4, 2)

To determine

To find: The volume of the parallelepiped with adjacent edges PQ, PR and PS.

Explanation

Given:

P(3,0,1),Q(1,2,5),R(5,1,1) and S(0,4,2) .

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)

Consider the adjacent edges as a=PQ , b=PR and c=PS .

Find a=PQ .

a=PQ=Q(1,2,5)P(3,0,1)=(13),(20),(51)=4,2,4

Find b=PR .

b=PR=R(5,1,1)P(3,0,1)=(53),(10),(11)=2,1,2

Find c=PS .

c=PS=S(0,4,2)P(3,0,1)=(03),(40),(21)=3,4,1

Modify equation (1)

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