Question

The resultant of $\overrightarrow{A}$ and $\overrightarrow{B}$ makes an angle $\alpha$ with $\overrightarrow{A}$ and an angle $\beta$ with $\overrightarrow{B}$ , then :-

• A. $\alpha <\beta$
• B. $\alpha <\beta$ if $A<B$
• C. $\alpha <\beta$ if $A>B$
• D. $\alpha <\beta$ if $A=B$

Answer 1

The correct option is C $\alpha <\beta$ if $A>B$

Here, $A=R\cos \alpha$ and $B=R\cos \beta$

So, $A=\frac{B}{\cos \beta }\cos \alpha$

or $\frac{A}{B}=\frac{\cos \alpha }{\cos \beta }$

If $A=B\Rightarrow \alpha =\beta$

If $A<B,1<\frac{\cos \alpha }{\cos \beta }\Rightarrow \alpha >\beta$

If $A>B,1>\frac{\cos \alpha }{\cos \beta }\Rightarrow \alpha <\beta$