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Question
Solution
\[\text{ We know } \]
\[ \left( \vec{a} . \vec{b} \right)^2 + \left| \vec{a} \times \vec{b} \right|^2 = \left| \vec{a} \right|^2 \left| \vec{b} \right|^2 \]
\[ \Rightarrow \left( 60 \right)^2 + \left| \vec{a} \times \vec{b} \right|^2 = \left( 13 \right)^2 \times 5^2 ( \because \vec{a} . \vec{b} = 60, \left| \vec{a} \right| = 13 \text{ and } \left| \vec{b} \right| = 5)\]
\[ \Rightarrow 3600 + \left| \vec{a} \times \vec{b} \right|^2 = 4225\]
\[ \Rightarrow \left| \vec{a} \times \vec{b} \right|^2 = 625\]
\[ \Rightarrow \left| \vec{a} \times \vec{b} \right| = 25\]
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