Question

Resultant of non-Zero vectors A and B makes angle $\alpha$ and $\beta$ with $\underset{A}{\overset{}{\to }}and\underset{B}{\overset{}{\to }}$ respectively.If
$|\underset{A}{\overset{}{\to }}|>|\underset{B}{\overset{}{\to }}|$

• A. $\alpha >\beta$
• B. $\beta >\alpha$
• C. $\frac{alpha}{\beta }=\frac{|\underset{B}{\overset{}{\to }}|}{|\underset{A}{\overset{}{\to }}|}$
• D. No definite inequality can be written between $\alpha and\beta$

Answer 1

The correct option is B $\beta >\alpha$

Form the figure, component of resultant vector

$\overrightarrow{A}=\overrightarrow{R}\cos \alpha$

$\overrightarrow{B}=\overrightarrow{R}\cos \beta$

If $\alpha <\beta$

Then, $\cos \alpha >\cos \beta$

$\overrightarrow{R}\text{cos}\alpha >\overrightarrow{R}\text{cos}\beta$

Hence, $hence,\overrightarrow{A}>\overrightarrow{B}$

So, we can say that, if $\overrightarrow{A}>\overrightarrow{B},\alpha <\beta$