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Mathematics Question on Vector Algebra

The volume of the parallelopiped whose sides are given by OA→=2i^−3j^,OB→=i^+j^−k^,OC→=3i^−k^\overrightarrow{OA}=2\widehat{i}-3\widehat{j},\overrightarrow{OB}=\widehat{i}+\widehat{j}-\widehat{k},\overrightarrow{OC}=3\widehat{i}-\widehat{k} is

A

413\frac{4}{13}

B

4

C

27\frac{2}{7}

D

None of these

Answer

4

Explanation

Solution

The volume of parallelopiped =[a→b→c→]=2−30\11−1\30−1=[\overrightarrow{a}\overrightarrow{b}\overrightarrow{c}]=\begin{array}|2&-3&0\\\1&1&-1\\\3&0&-1\\\\\end{array}
=2 (-1) + 3 (-1 + 3) = -2 + 6 = 4