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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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