Question

The coordinates of the foot of the perpendicular drawn from the point \( (0, 1, 2) \) on the \( x \)-axis are given by:

• A. \( (1, 0, 0) \)
• B. \( (2, 0, 0) \)
• C. \( (\sqrt{5}, 0, 0) \)
• D. \( (0, 0, 0) \)

Hint:

When finding the foot of the perpendicular from a point to an axis, keep the axis' coordinates fixed and set the other coordinates to zero.

Answer 1

The Correct Option is D

Step 1: Define the \( x \)-axis.
The \( x \)-axis consists of all points where the coordinates are of the form \( (x, 0, 0) \), where \( x \) is any real number. Step 2: Foot of the perpendicular.
The foot of the perpendicular from the point \( (0, 1, 2) \) onto the \( x \)-axis represents the closest point on the \( x \)-axis. Since the perpendicular from \( (0, 1, 2) \) to the \( x \)-axis drops to \( x = 0 \), the foot of the perpendicular has the coordinates: \[ (0, 0, 0). \] Step 3: Conclusion.
Thus, the foot of the perpendicular is: \[ \boxed{(0, 0, 0)}. \]