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Question
If \[\vec{a} \text{ and } \vec{b}\] are two vectors of the same magnitude inclined at an angle of 60° such that \[\vec{a} . \vec{b} = 8,\] write the value of their magnitude.
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Solution
\[\text{ Given that }\]
\[\left| \vec{a} \right| = \left| \vec{b} \right| \]
\[\text{ and } \vec{a} \text{ and } \vec{b} \text{ are inclined at an angle of } 60° \]
\[\text{ Also, given that }\]
\[ \vec{a} . \vec{b} = 8\]
\[ \Rightarrow \left| \vec{a} \right| \left| \vec{b} \right| \cos 60° = 8\]
\[ \Rightarrow \left| \vec{a} \right|\left| \vec{a} \right| \left( \frac{1}{2} \right) = 8\]
\[ \Rightarrow \left| \vec{a} \right|^2 = 16\]
\[ \Rightarrow \left| \vec{a} \right| = 4\]
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