If \(\vec{a}\) is a unit vector and \((\vec{x} - \vec{a}) \cdot (\vec{x} + \vec{a}) = 8\) then \(|\vec{x}|\) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 3
Expanding the dot product, the middle terms cancel because \(\vec{x} \cdot \vec{a} = \vec{a} \cdot \vec{x}\):
\((\vec{x} - \vec{a}) \cdot (\vec{x} + \vec{a}) = |\vec{x}|^2 - |\vec{a}|^2\)
Since \(\vec{a}\) is a unit vector, \(|\vec{a}| = 1\):
\(|\vec{x}|^2 - 1 = 8\)
\(|\vec{x}|^2 = 9\)
\(|\vec{x}| = 3\)