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

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

Question

(C) Given that $\vec{R_1} = \vec{A} + \vec{B}$.Taking the magnitude squared: $R_1^2 = |\vec{A} + \vec{B}|^2 = A^2 + B^2 + 2AB \cos 	heta$,where $	he

Vedclass · Accepted Answer

$2(A^2 + B^2)$

Vedclass · Answer

(C) Given that $\vec{R_1} = \vec{A} + \vec{B}$.Taking the magnitude squared: $R_1^2 = |\vec{A} + \vec{B}|^2 = A^2 + B^2 + 2AB \cos 	heta$,where $	heta$ is the angle between $\vec{A}$ and $\vec{B}$.When vector $\vec{B}$ is reversed,the new resultant is $\vec{R_2} = \vec{A} - \vec{B}$.Taking the magnitude squared: $R_2^2 = |\vec{A} - \vec{B}|^2 = A^2 + B^2 - 2AB \cos 	heta$.Adding the two equations:$R_1^2 + R_2^2 = (A^2 + B^2 + 2AB \cos 	heta) + (A^2 + B^2 - 2AB \cos 	heta)$.$R_1^2 + R_2^2 = 2A^2 + 2B^2 = 2(A^2 + B^2)$.

The resultant of two vectors $\vec{A}$ and $\vec{B}$ is $\vec{R_1}$. If vector $\vec{B}$ is reversed,the resultant becomes $\vec{R_2}$. What is the value of $R_1^2 + R_2^2$?

Similar Questions

Two vectors $\vec{A}$ and $\vec{B}$ are such that $\vec{A} + \vec{B} = \vec{A} - \vec{B}$. Then:

What is the angle between $\overrightarrow P$ and the resultant of $(\overrightarrow P + \overrightarrow Q)$ and $(\overrightarrow P - \overrightarrow Q)$?

The resultant of two vectors $\vec{A}$ and $\vec{B}$ is $\vec{C}$. If the magnitude of $\vec{B}$ is doubled,the new resultant vector becomes perpendicular to $\vec{A}$. Then,the magnitude of $\vec{C}$ is:

Two vectors of the same magnitude have a resultant equal to either of the two vectors. The angle between the two vectors is: (in $^{\circ}$)

At what angle must the two forces $(x + y)$ and $(x - y)$ act so that the resultant may be $\sqrt{x^2 + y^2}$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module