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If \(\rm \vec a\) is a unit vector and \(\rm \left(\vec x + 2\vec a\right) \cdot \left(\vec x - 2\vec a\right) = 12\), then find \(|\rm \vec x |\).1. 42. 73. 84. 2 |
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Answer» Correct Answer - Option 1 : 4 Concept: \(\rm \left(\vec a + \vec b\right) \cdot \left(\vec a - \vec b\right) = \left|\vec a\right|^2-\left|\vec b\right|^2\) If \(\rm \vec u\) is a unit vector, then \(\rm \left|\vec u\right|=1\).
Calculation: It is given that \((\rm \vec x + \rm 2\vec a) \cdot (\rm \vec x - \rm 2\vec a) = 12\). ⇒ \(\rm \left|\vec x\right|^2 - 4\left|\vec a\right|^2 = 12\) Since \(\rm \vec a\) is a unit vector, we get: ⇒ \(\rm \left|\vec x\right|^2 - 4= 12\) ⇒ \(\rm \left|\vec x\right|^2 =16\) ⇒ \(|\rm \vec x |\) = 4 |
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