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Find the equation of the projection o...

Find the equation of the projection of the line `(x-1)/2=(y+1)/(-1)=(z-3)/4` on the plane `x+2y+z=9.`

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To find the equation of the projection of the line given by \((x-1)/2 = (y+1)/(-1) = (z-3)/4\) onto the plane defined by \(x + 2y + z = 9\), we will follow these steps: ### Step 1: Identify the direction vector of the line The line is given in symmetric form: \[ \frac{x-1}{2} = \frac{y+1}{-1} = \frac{z-3}{4} \] From this, we can extract the direction vector \(\mathbf{a}\) of the line: ...
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