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in Three Dimensional Geometry by (28.2k points)
closed by

\(\overline {OA}\)= i + 2j + 3k

\(\overline{OB}\) = i – 2j + 4k

\(\overline {OC}\) = 2i + 3j + k

are adjacent sides of the parallelopiped.

  1. Find the base area of the parallelopiped. 
    (Base determined by \(\overline {OA}\) and \(\overline{OB}\)
  2. Find the volume of the parallelopiped.
  3. Find the height of the parallelopiped.

1 Answer

+1 vote
by (28.9k points)
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Best answer

1. \(\overline{OA} \times \overline {OB}\)  =

= 14i – j – 4k
Base area = |l4i – j – 4k|

\(\sqrt{196+1+16} = \sqrt{213}\)

2. Volume of the parallelopiped is

= (14i – j – 4k).(2i + 3 j + k)

= 28 – 3 – 4 = 21.

3. Height = \(\frac{volume}{base\, area}\) = \(\frac{21}{\sqrt{23}}\).

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