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

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(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

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

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 $\vec{B}$?

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