Question

the resultant of two vectors $\overline{A}\text{and}\overline{B}$ makes an angle $\alpha \text{with}\overline{A}$ and $\beta with\overline{B}$. If $A=|\overline{A}|,B=|\overline{B}|$, then

• A. $\alpha =\beta$ always
• B. $\alpha <\beta$ id A < B
• C. $\alpha <\beta$ id A > B
• D. $\alpha \ne \beta$ always

Answer 1

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

$\text{Given}:$ The angle of resultant with Vector A = $\alpha$

The angle of vector B with Resultant = $\beta$

$\text{Solution}:$

From the given data, the total angle between Vector A and Vector B = $\alpha +\beta$

Now,

$A=Rcos\alpha$

$B=Rcos\beta$

If $\alpha <\beta$

Then,

$cos\alpha >cos\beta$

$=Rcos\alpha >Rcos\beta$

Hence,

A > B

thus, it can be said

A > B and $\alpha <\beta$

$\text{Hence C is the correct option}$