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Let \( \vec{r} \) be a position vector of a variable point in Cartesian \( O X Y \) plane such that \( \vec{r} \cdot(10 \hat{j}-8 \hat{i}-\vec{r})=40 \) and
\( \mathrm{P} \) \( p_{1}=\max \left\{|\vec{r}+2 \hat{i}-3 \hat{j}|^{2}\right\}, p_{2}=\min \left\{|\vec{r}+2 \hat{i}-3 \hat{j}|^{2}\right\} \). A tangent line is drawn to the curve \( y=8 / x^{2} \) at point \( A \)

W. with abscissa 2 . The drawn line cuts the \( x \)-axis at a point \( B \). \( p_{1}+p_{2} \) is equal to
(1) 2
(2) 10
(3) 18
(4) 5
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