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Find the vector equation of a line pa...

Find the vector equation of a line passing through `3 hat i-5 hat j+7 hat k` and perpendicular to theplane `3x-4y+5z=8.`

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To find the vector equation of a line that passes through the point \( \mathbf{A} = 3\hat{i} - 5\hat{j} + 7\hat{k} \) and is perpendicular to the plane given by the equation \( 3x - 4y + 5z = 8 \), we can follow these steps: ### Step 1: Identify the normal vector of the plane The equation of the plane can be written in the form \( Ax + By + Cz = D \), where \( A, B, C \) are the coefficients of \( x, y, z \) respectively. From the equation \( 3x - 4y + 5z = 8 \), we can identify the normal vector \( \mathbf{n} \) of the plane as: \[ \mathbf{n} = 3\hat{i} - 4\hat{j} + 5\hat{k} \] ...
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