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Let Q be the reflection of the point P(2, 3, 4) across the plane x − 2y + 5z = 6. The equation of the line joining P and Q is

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

Correct answer: (x − 2)/1 = (y − 3)/−2 = (z − 4)/5

Solution

The correct option represents the direction vector of the line connecting points P and Q, where the reflection across the plane results in a change in the y-coordinate while keeping the x and z coordinates consistent with the original point. This indicates that the line's slope in the y-direction is negative, confirming the correct ratios in the equation.

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