Perpendiculars are drawn from points on the line (x+2)/(2) = (y+1)/(-1) = (z)/(3) to the plane x + y + z = 3. The feet of perpendiculars lie on the line -

(x)/(5) = (y-1)/(8) = (z-2)/(-13)
(x)/(2) = (y-1)/(3) = (z-2)/(-5)
(x)/(4) = (y-1)/(3) = (z-2)/(-7)
(x)/(2) = (y-1)/(-7) = (z-2)/(5)

Correct answer: (x)/(2) = (y-1)/(-7) = (z-2)/(5)

Solution

The feet of perpendiculars from the given line to the plane lie on a line whose direction ratios are derived from the normal vector of the plane and the line's direction. This matches the equation (x)/(2) = (y-1)/(-7) = (z-2)/(5).

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