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The image of the line (x−1)/3 = (y−3)/1 = (z−4)/(−5) in the plane 2x − y + z + 3 = 0 is the line:

1. (x−3)/(−3) = (y+5)/(−1) = (z−2)/5
2. (x+3)/3 = (y−5)/1 = (z−2)/(−5)
3. (x+3)/3 = (y−5)/(−1) = (z+2)/5
4. (x−3)/3 = (y+5)/1 = (z−2)/(−5)

Correct answer: (x+3)/3 = (y−5)/1 = (z−2)/(−5)

Solution

The correct option represents the image of the original line under the transformation defined by the plane equation, ensuring that the direction ratios and a point on the line satisfy the plane's constraints.

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