Question

Vector $\overset{\rightarrow}{R}$is the resultant of the vectors $\overset{\rightarrow}{A}$and $\overset{\rightarrow}{B}$. Ratio of minimum value of |$\overset{\rightarrow}{R}$| and maximum value of |$\overset{\rightarrow}{R}$| is $\frac{1}{4}$. Then $\frac{|\overset{\rightarrow}{A}|}{|\overset{\rightarrow}{B}|}$may be –

• A. $\frac{4}{1}$
• B. $\frac{2}{1}$
• C. $\frac{3}{5}$
• D. $\frac{1}{4}$

Answer 1

Answer: (C)

$\frac{3}{5}$

Answer 2

$\frac{|\overset{\rightarrow}{R}|_{\min}}{|R|_{\max}}$= $\frac{1}{4}$= $\frac{||\overset{\rightarrow}{A}| - |\overset{\rightarrow}{B}||}{||\overset{\rightarrow}{A}| + |\overset{\rightarrow}{B}||}$

$|\overset{\rightarrow}{A}| + |\overset{\rightarrow}{B}|$= 4 |$|\overset{\rightarrow}{A}| - |\overset{\rightarrow}{B}|$|

If | $\overset{\rightarrow}{A}$| > | $\overset{\rightarrow}{B}$|

| $\overset{\rightarrow}{A}$| + | $\overset{\rightarrow}{B}$| = 4 ( | $\overset{\rightarrow}{A}$| – | $\overset{\rightarrow}{B}$| )

3 | $\overset{\rightarrow}{A}$| = 5 | $\overset{\rightarrow}{B}$| ̃ $\frac{|\overset{\rightarrow}{A}|}{|\overset{\rightarrow}{B}|}$= $\frac{5}{3}$

If | $\overset{\rightarrow}{B}$| > | $\overset{\rightarrow}{A}$ |

$|\overset{\rightarrow}{A}| + |\overset{\rightarrow}{B}|$= 4 ( $|\overset{\rightarrow}{B}| - |\overset{\rightarrow}{A}|$)

$\frac{|\overset{\rightarrow}{A}|}{|\overset{\rightarrow}{B}|}$ = $\frac{3}{5}$