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(D) The maximum resultant magnitude of two vectors $A$ and $B$ is given by $R_{max} = A + B$.The minimum resultant magnitude of two vectors $A$ and $B

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$\frac{n+1}{n-1}$

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(D) The maximum resultant magnitude of two vectors $A$ and $B$ is given by $R_{max} = A + B$.The minimum resultant magnitude of two vectors $A$ and $B$ is given by $R_{min} = A - B$.According to the problem,$R_{max} = n \cdot R_{min}$.Substituting the expressions,we get $A + B = n(A - B)$.Expanding the equation: $A + B = nA - nB$.Rearranging the terms to group $A$ and $B$: $A - nA = -nB - B$.$A(1 - n) = -B(n + 1)$.Dividing both sides by $B(1 - n)$: $\frac{A}{B} = \frac{-(n + 1)}{1 - n}$.Multiplying the numerator and denominator by $-1$: $\frac{A}{B} = \frac{n + 1}{n - 1}$.

The magnitudes of two vectors are $A$ and $B$ $(A > B)$. If the maximum resultant magnitude of the two vectors is $n$ times their minimum resultant magnitude,then $\frac{A}{B} =$

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