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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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 $\alpha + \beta \neq 90^o$).

Similar Questions

Two forces $F_1 = 3 \ N$ at $0^o$ and $F_2 = 5 \ N$ at $60^o$ act on a body. Then a single force that would balance the two forces must have a magnitude of .......... $N$

The vectors $\vec{A}$ and $\vec{B}$ are such that $|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|$. The angle between the two vectors is: (in $^{\circ}$)

What vector must be added to the two vectors $\hat{i} - 2\hat{j} + 2\hat{k}$ and $2\hat{i} + \hat{j} - \hat{k}$ so that the resultant may be a unit vector along the $X$-axis?

Which of the following relations is true for two unit vectors $\hat{A}$ and $\hat{B}$ making an angle $\theta$ to each other?

The figure shows three vectors $\vec{a}, \vec{b}$ and $\vec{c}$,where $R$ is the midpoint of $PQ$. Which of the following relations is correct?

Vedclass Test Series

Exam Paper Generator

Online Exam Module