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Question
Write the value of the area of the parallelogram determined by the vectors \[2 \hat{ i } \text{ and } 3 \hat{ j } .\]
Solution
\[\text{ Let } :\]
\[ \vec{a} =2 \hat{ i } \]
\[ \vec{b} =3 \hat{ j } \]
\[ \vec{a} \times \vec{b} = 6 \left( \hat{ i } \times \hat{ j } \right)\]
\[ = 6 \hat{ k } \]
\[\text{ Area of the parallelogram } = \left| \vec{a} \times \vec{b} \right|\]
\[ = 6 \left| \hat{ k } \right|\]
\[ = 6\left( 1 \right)\]
\[ = 6 \text { sq. units } \]
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