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

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(C) Let the vectors be $\vec{A}$ and $\vec{B}$. The resultant is $\vec{C} = \vec{A} + \vec{B}$.Taking the dot product of $\vec{C}$ with itself,we get

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$B$

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(C) Let the vectors be $\vec{A}$ and $\vec{B}$. The resultant is $\vec{C} = \vec{A} + \vec{B}$.Taking the dot product of $\vec{C}$ with itself,we get $C^2 = A^2 + B^2 + 2\vec{A} \cdot \vec{B}$.When the magnitude of $\vec{B}$ is doubled,the new resultant is $\vec{C}' = \vec{A} + 2\vec{B}$.It is given that $\vec{C}'$ is perpendicular to $\vec{A}$,so $\vec{A} \cdot \vec{C}' = 0$.$\vec{A} \cdot (\vec{A} + 2\vec{B}) = 0 \implies A^2 + 2\vec{A} \cdot \vec{B} = 0$.This implies $2\vec{A} \cdot \vec{B} = -A^2$.Substituting this into the expression for $C^2$:$C^2 = A^2 + B^2 - A^2 = B^2$.Therefore,the magnitude of $\vec{C}$ is $B$.

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

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