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Find the equation of the line which pas...

Find the equation of the line which passes through the point (1, 2, 3) and is parallel to the vector `3 hat i+2 hat j-2 hat k`.

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To find the equation of the line that passes through the point \( (1, 2, 3) \) and is parallel to the vector \( \vec{v} = 3\hat{i} + 2\hat{j} - 2\hat{k} \), we can use the parametric form of the line in three-dimensional geometry. ### Step-by-Step Solution: 1. **Identify the Point and Direction Vector**: - The point through which the line passes is \( P(1, 2, 3) \). - The direction vector of the line is \( \vec{d} = 3\hat{i} + 2\hat{j} - 2\hat{k} \). ...
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