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Question
Find \[\left| \vec{a} - \vec{b} \right|\]
\[\left| \vec{a} \right| = 3, \left| \vec{b} \right| = 4 \text{ and } \vec{a} \cdot \vec{b} = 1\]
Sum
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Solution
\[\text{ Given that }\]
\[\left| \vec{a} \right| = 3, \left| \vec{b} \right| = 4 \text{ and } \vec{a} . \vec{b} = 1.................. \left( 1 \right)\]
\[\text{ We know that }\]
\[ \left| \vec{a} - \vec{b} \right|^2 = \left| \vec{a} \right|^2 + \left| \vec{b} \right|^2 - 2 \vec{a} . \vec{b} \]
\[ = 3^2 + 4^2 - 2 \left( 1 \right)............... \left[ \text{ Using } \left( 1 \right) \right]\]
\[ = 9 + 16 - 2\]
\[ = 23\]
\[ \therefore \left| \vec{a} - \vec{b} \right| = \sqrt{23}\]
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