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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 \(3\hat{i} + 2\hat{j} - 2\hat{k}\), we can follow these steps: ### Step 1: Identify the point and the direction vector The point through which the line passes is given as \(P(1, 2, 3)\). The direction vector of the line is given as \( \mathbf{d} = 3\hat{i} + 2\hat{j} - 2\hat{k}\). ### Step 2: Write the position vector of the point The position vector of the point \(P(1, 2, 3)\) can be expressed as: \[ ...
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