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soopo

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## Homework Statement

Let P = (2, 2, 0), Q = (0, 4, 1) and R = (-1, 2, 3) in the space [tex] \Re^{3}.

[/tex]

a) Determine the area of the rectangle determined by vectors [tex]\overrightarrow{PQ}[/tex] and [tex]\overrightarrow{PR}[/tex].

b) Determine the volume of the tetrahedral determined by vectors [tex]\overrightarrow{PQ}[/tex] and [tex]\overrightarrow{PR}[/tex], and the origin O, OPQR.

## The Attempt at a Solution

a)

[tex]

|\overrightarrow{PQ}| = \sqrt {4 + 4 +1} = 3

[/tex]

[tex]

|\overrightarrow{PR}| = \sqrt {9 + 0 + 9} = 3 \sqrt {2}

[/tex]

[tex]

Area = |\overrightarrow{PQ}| * |\overrightarrow{PR}|

= 9 \sqrt {2}

[/tex]

b)

[tex]

Volume = Area * |\overrightarrow{RO}|

|\overrightarrow{RO}| = \sqrt {1 + 4 + 9}

= \sqrt {14}

[/tex]

The volume is

[tex]

Volume = 9 \sqrt{2} * \sqrt {14}

= 18 \sqrt {7}

[/tex]

Please, comment any mistakes.

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