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प्रश्न
If \[\vec{a}\] is a unit vector, then find \[\left| \vec{x} \right|\] in each of the following.
\[\left( \vec{x} - \vec{a} \right) \cdot \left( \vec{x} + \vec{a} \right) = 8\]
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उत्तर
\[\text{ Given that } \vec{a} \text{ is a unit vector }.\]
\[ \Rightarrow \left| \vec{a} \right| = 1 . . . \left( 1 \right)\]
\[ \left( \vec{x} - \vec{a} \right) . \left( \vec{x} + \vec{a} \right) = 8\]
\[ \Rightarrow \left| \vec{x} \right|^2 - \left| \vec{a} \right|^2 = 8\]
\[ \Rightarrow \left| \vec{x} \right|^2 - 1^2 = 8 .................\left[ \text{ From } (1) \right]\]
\[ \Rightarrow \left| \vec{x} \right|^2 = 9\]
\[ \Rightarrow \left| \vec{x} \right| = 3\]
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