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If $\mathbf{r}_1=2 \hat{\mathbf{x}}, \mathbf{r}_2=2 \hat{\mathbf{y}}$, where $\hat{\mathbf{x}}$ and $\hat{\mathbf{y}}$ are unit vectors along the $X$-axis and $Y$-axis respectively, then the magnitude of $\mathbf{r}_1+\mathbf{r}_2$ is
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$2 \sqrt{2}$
$\begin{array}{ll}\text { Given, } \mathbf{r}_1=2 \hat{\mathbf{x}} \Rightarrow \mathbf{r}_2=2 \hat{\mathbf{y}} \\\therefore \mathbf{r}_1+\mathbf{r}_2=2 \hat{\mathbf{x}}+2 \hat{\mathbf{y}} \\ \therefore \left|\mathbf{r}_1+\mathbf{r}_2\right|=\sqrt{2^2+2^2}=\sqrt{8}=2 \sqrt{2}\end{array}$
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