The magnitude of the X and Y components of ve | vedclass

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(A) Let $\vec{A} + \vec{B} = \vec{R}$.Given the components of $\vec{A}$ are $A_x = 7$ and $A_y = 6$.Given the components of the resultant vector $\vec

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$5$

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(A) Let $\vec{A} + \vec{B} = \vec{R}$.Given the components of $\vec{A}$ are $A_x = 7$ and $A_y = 6$.Given the components of the resultant vector $\vec{R}$ are $R_x = 11$ and $R_y = 9$.Since $\vec{R} = \vec{A} + \vec{B}$,we have $\vec{B} = \vec{R} - \vec{A}$.The components of $\vec{B}$ are:$B_x = R_x - A_x = 11 - 7 = 4$$B_y = R_y - A_y = 9 - 6 = 3$The magnitude of $\vec{B}$ is given by $|\vec{B}| = \sqrt{B_x^2 + B_y^2}$.$|\vec{B}| = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5$.

The magnitude of the $X$ and $Y$ components of $\vec{A}$ are $7$ and $6$ respectively. Also,the magnitude of the $X$ and $Y$ components of $\vec{A} + \vec{B}$ are $11$ and $9$ respectively. What is the magnitude of $\vec{B}$?

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