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Find the vector equation of the plane pa...

Find the vector equation of the plane passing through the intersection of the planes` -> rdot(2 hat i+2 hat j-3 hat k)=7, -> rdot(2 hat i+5 hat j+3 hat k)=9`and through the point (2, 1, 3).

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To find the vector equation of the plane passing through the intersection of the given planes and through the point (2, 1, 3), we can follow these steps: ### Step 1: Write the equations of the given planes The equations of the two planes are given as: 1. \( \vec{r} \cdot (2 \hat{i} + 2 \hat{j} - 3 \hat{k}) = 7 \) 2. \( \vec{r} \cdot (2 \hat{i} + 5 \hat{j} + 3 \hat{k}) = 9 \) ### Step 2: Express the equation of the plane through the intersection ...
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