Question

Let \( \vec{a} \) be a unit vector. If \( (\vec{x} - \vec{a}) \cdot (\vec{x} + \vec{a}) = 12 \), then the magnitude of \( \vec{x} \) is:

• A. \( \sqrt{8} \)
• B. \( \sqrt{9} \)
• C. \( \sqrt{10} \)
• D. \( \sqrt{13} \)
• E. \( \sqrt{12} \)

Hint:

Remember the vector identity \( (\vec{u} - \vec{v}) \cdot (\vec{u} + \vec{v}) = |\vec{u}|^2 - |\vec{v}|^2 \). It is the vector equivalent of the algebraic difference of squares formula \( (a-b)(a+b) = a^2 - b^2 \).

Answer 1

The Correct Option is D