Vector R→ is the resultant of the vectors A→ and B→ . The ratio of the maximum value of R→ to the minimum value of R→ is 31 . The A→B→ may be equal to-

A→+B→maxA→+B→min=A→+B→A→-B→=31If A→>B→A→+B→A→-B→=31⇒A→B→=21If A→<B→A→+B→B→-A→=31⇒A→B→=12

Vector R→ is the resultant of the vectors A→ and B→ . The ratio of the maximum value of R→ to the minimum value of R→ is 31 . The A→B→ may be equal to-

A→+B→maxA→+B→min=A→+B→A→-B→=31If A→>B→A→+B→A→-B→=31⇒A→B→=21If A→<B→A→+B→B→-A→=31⇒A→B→=12

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Vector $\vec{R}$ is the resultant of the vectors $\vec{A}$ and $\vec{B}$ . The ratio of the maximum value of $|\vec{R}|$ to the minimum value of $|\vec{R}|$ is $\frac{3}{1}$ . The $\frac{|\vec{A}|}{|\vec{B}|}$ may be equal to-

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$\frac{2}{1}$

$\frac{4}{1}$

$\frac{1}{2}$

$\frac{3}{1}$

answer is A, B.

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Detailed Solution

$\frac{{|\vec{A} + \vec{B}|}_{m a x}}{{|\vec{A} + \vec{B}|}_{m i n}} = \frac{|\vec{A}| + |\vec{B}|}{|\vec{A}| - |\vec{B}|} = \frac{3}{1}$

If $|\vec{A}| > |\vec{B}|$

$\frac{|\vec{A}| + |\vec{B}|}{|\vec{A}| - |\vec{B}|} = \frac{3}{1} \Rightarrow \frac{|\vec{A}|}{|\vec{B}|} = \frac{2}{1}$

If $|\vec{A}| < |\vec{B}|$

$\frac{|\vec{A}| + |\vec{B}|}{|\vec{B}| - |\vec{A}|} = \frac{3}{1} \Rightarrow \frac{|\vec{A}|}{|\vec{B}|} = \frac{1}{2}$

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Vector R→ is the resultant of the vectors A→ and B→ . The ratio of the maximum value of R→ to the minimum value of R→ is 31 . The A→B→ may be equal to-

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Vector $\vec{R}$ is the resultant of the vectors $\vec{A}$ and $\vec{B}$ . The ratio of the maximum value of $|\vec{R}|$ to the minimum value of $|\vec{R}|$ is $\frac{3}{1}$ . The $\frac{|\vec{A}|}{|\vec{B}|}$ may be equal to-