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

(A) Let the resultant vector be $\vec{R} = \vec{A} + \vec{B}$.Given that $\vec{R} \perp \vec{A}$,the dot product $\vec{R} \cdot \vec{A} = 0$.Substitut

Vedclass · Accepted Answer

$\cos^{-1}\left(-\frac{A}{B}\right)$

Vedclass · Answer

(A) Let the resultant vector be $\vec{R} = \vec{A} + \vec{B}$.Given that $\vec{R} \perp \vec{A}$,the dot product $\vec{R} \cdot \vec{A} = 0$.Substituting $\vec{R} = \vec{A} + \vec{B}$,we get $(\vec{A} + \vec{B}) \cdot \vec{A} = 0$.Expanding the dot product: $\vec{A} \cdot \vec{A} + \vec{B} \cdot \vec{A} = 0$.This simplifies to $A^2 + AB \cos 	heta = 0$,where $	heta$ is the angle between $\vec{A}$ and $\vec{B}$.Solving for $\cos 	heta$: $\cos 	heta = -\frac{A^2}{AB} = -\frac{A}{B}$.Therefore,$	heta = \cos^{-1}\left(-\frac{A}{B}ight)$.

The resultant of two vectors $\vec{A}$ and $\vec{B}$ is perpendicular to $\vec{A}$. What is the angle between $\vec{A}$ and $\vec{B}$?

Similar Questions

Let the two forces have equal magnitude $A$. If the magnitude of the resultant is $\frac{2A}{3}$,then the angle between those two forces is:

$A$ vector $\vec{A}$ when added to the sum of the vectors $(\hat{i} - 2\hat{j} + 2\hat{k})$ and $(-2\hat{i} + \hat{j} - \hat{k})$ gives a unit vector along the $Y$-axis. The magnitude of vector $\vec{A}$ is

Let $\vec{A}$ and $\vec{B}$ be two non-zero vectors of different magnitudes. Which one of the following is the correct equation?

The angle between two forces of equal magnitude $R$,if the magnitude of their resultant is $\frac{R}{2}$,is:

If the sum of two unit vectors is a unit vector,then the magnitude of their difference is

Vedclass Test Series

Exam Paper Generator

Online Exam Module