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(B) Given that the components of vector $\vec{P}$ are $P_x = 1$ and $P_y = 3$. Thus,$\vec{P} = 1\hat{i} + 3\hat{j}$.Let the resultant vector be $\vec{

Vedclass · Accepted Answer

$5$

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(B) Given that the components of vector $\vec{P}$ are $P_x = 1$ and $P_y = 3$. Thus,$\vec{P} = 1\hat{i} + 3\hat{j}$.Let the resultant vector be $\vec{R} = \vec{P} + \vec{Q}$. The components of $\vec{R}$ are given as $R_x = 5$ and $R_y = 6$. Thus,$\vec{R} = 5\hat{i} + 6\hat{j}$.We know that $\vec{Q} = \vec{R} - \vec{P}$.Substituting the values: $\vec{Q} = (5\hat{i} + 6\hat{j}) - (1\hat{i} + 3\hat{j}) = (5-1)\hat{i} + (6-3)\hat{j} = 4\hat{i} + 3\hat{j}$.The magnitude of $\vec{Q}$ is $|\vec{Q}| = \sqrt{Q_x^2 + Q_y^2} = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5$.Therefore,the correct option is $B$.

The $x$ and $y$ components of vector $\vec{P}$ have magnitudes $1$ and $3$,and the $x$ and $y$ components of the resultant of $\vec{P}$ and $\vec{Q}$ have magnitudes $5$ and $6$ respectively. What is the magnitude of $\vec{Q}$?

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