# Find the volume of a parallelopiped whose coterimus edges are represented by the vectors ikikiji^+k^,i^+k^,i^+j^. Also find volume of tetrahedron having these coterminus edges. - Mathematics and Statistics

Sum

Find the volume of a parallelopiped whose coterimus edges are represented by the vectors hat"i" + hat"k", hat"i" + hat"k", hat"i" + hat"j". Also find volume of tetrahedron having these coterminus edges.

#### Solution

Let bar"a" = hat"j" + hat"k", bar"b" = hat"i" + hat"k" and bar"c" = hat"i" + hat"j" be the coterminus edges of a parallelopiped.

Then volume of the parallelopiped = [bar"a"  bar"b"  bar"c"]

= |(0,1,1),(1,0,1),(1,1,0)|

= 0(0 - 1)- 1(0 - 1) + 1(1 - 0)

= 0 + 1 + 1 = 2 cu units

Also, volume of tetrahedron = 1/6 [bar"a"  bar"b"  bar"c"]

= 1/6(2) = 1/3 cubic units

Concept: Section Formula
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