Two vectors of magnitude 3 and 4 have a resul | vedclass

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(C) Let the two vectors be $\vec{A}$ and $\vec{B}$ with magnitudes $A = 3$ and $B = 4$. Let $\vec{R}$ be their resultant.If we resolve both vectors al

Vedclass · Accepted Answer

$\frac{\sin \alpha}{\sin \beta} = \frac{4}{3}$

Vedclass · Answer

(C) Let the two vectors be $\vec{A}$ and $\vec{B}$ with magnitudes $A = 3$ and $B = 4$. Let $\vec{R}$ be their resultant.If we resolve both vectors along the direction perpendicular to the resultant $\vec{R}$,the sum of the components must be zero because the resultant has no component perpendicular to itself.Thus,the component of vector $3$ perpendicular to $\vec{R}$ must be equal in magnitude to the component of vector $4$ perpendicular to $\vec{R}$ in the opposite direction.Therefore,$3 \sin \alpha = 4 \sin \beta$.Rearranging the terms,we get $\frac{\sin \alpha}{\sin \beta} = \frac{4}{3}$.

Two vectors of magnitude $3$ and $4$ have a resultant which makes angles $\alpha$ and $\beta$ respectively with them (given $\alpha + \beta \neq 90^o$).

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