The resultant of \( \mathbf{A} \) and \( \mathbf{B} \) is \( \mathbf{R}_{\mathbf{1}} \). On reve...

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The resultant of \( \mathbf{A} \) and \( \mathbf{B} \) is \( \mathbf{R}_{\mathbf{1}} \). On reversing the vector \( \mathbf{B} \), the resultant becomes \( \mathbf{R}_{2} \). What is the value of \( R_{1}^{2}+R_{2}^{2} \) ?
(a) \( A^{2}+B^{2} \)
(b) \( A^{2}-B^{2} \)
(c) \( 2\left(A^{2}+B^{2}\right) \)
(d) \( 2\left(A^{2}-B^{2}\right) \)
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