The resultant of two vectors vec{A} and vec{B | vedclass

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(C) Let the resultant vector be $\vec{R} = \vec{A} + \vec{B}$.By the law of sines in the triangle formed by vectors $\vec{A}$,$\vec{B}$,and $\vec{R}$,

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$\alpha  B$

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(C) Let the resultant vector be $\vec{R} = \vec{A} + \vec{B}$.By the law of sines in the triangle formed by vectors $\vec{A}$,$\vec{B}$,and $\vec{R}$,we have $\frac{A}{\sin \beta} = \frac{B}{\sin \alpha}$.This implies $\frac{\sin \alpha}{\sin \beta} = \frac{B}{A}$.If $A > B$,then $\frac{B}{A} Since $\alpha$ and $\beta$ are angles within a triangle,$\sin \alpha Therefore,the resultant vector is closer to the vector with the larger magnitude. Thus,if $A > B$,then $\alpha < \beta$.

The resultant of two vectors $\vec{A}$ and $\vec{B}$ makes an angle $\alpha$ with $\vec{A}$ and an angle $\beta$ with $\vec{B}$. Which of the following is true?

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