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The length of the projection of the line segment joining the points (5, −1, 4) and (4, −1, 3) on the plane, x + y + z = 7 is:

1. 2/3
2. 1/3
3. √(2/3)
4. 2/√3

Correct answer: √(2/3)

Solution

The projection of the line segment onto the plane is determined by the direction vector of the segment and the normal vector of the plane. By calculating the length of the projection using the formula involving the dot product of these vectors, we find that the correct length is √(2/3), which accounts for the angle between the segment and the plane.

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