Find the signed volume of the parallelepiped formed by the following triples of vectors

Chapter 5, Problem 2

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QUESTION:

Find the signed volume of the parallelepiped formed by the following triples of vectors in \(\mathbb{R}^{3}\).

a. x = (1, 2, 1), y = (2, 3, 1), z = (1, 0, 3)

b. x = (1, 1, 1), y = (2, 3, 4), z = (1, 1, 5)

c. x = (3,1, 2), y = (1, 0,3), z = (2, 1,1)

Questions & Answers

QUESTION:

Find the signed volume of the parallelepiped formed by the following triples of vectors in \(\mathbb{R}^{3}\).

a. x = (1, 2, 1), y = (2, 3, 1), z = (1, 0, 3)

b. x = (1, 1, 1), y = (2, 3, 4), z = (1, 1, 5)

c. x = (3,1, 2), y = (1, 0,3), z = (2, 1,1)

ANSWER:

Step 1 of 3

Volume of parallelogram formed by vectors given by:

For given vectors:

(a)

So, the required volume is .

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