Question:
The distance between the \( x \)-axis and the point \( (3, 12, 5) \) is:
The distance between the \( x \)-axis and the point \( (3, 12, 5) \) is:
Show Hint
The formula for distance from the $x$-axis is simply $\sqrt{y^2 + z^2}$. Similarly, distance from the $y$-axis is $\sqrt{x^2 + z^2}$.
Updated On: May 6, 2026
- \( 3 \)
- \( 13 \)
- \( 14 \)
- \( 12 \)
- \( 5 \)
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The Correct Option is B
Solution and Explanation
Concept:
The distance of a point \( (x, y, z) \) from the \( x \)-axis is determined by the length of the perpendicular dropped to that axis. On the \( x \)-axis, the \( y \) and \( z \) coordinates are zero. The projection of \( (x, y, z) \) on the \( x \)-axis is \( (x, 0, 0) \).
Step 1: Identify the projection on the \( x \)-axis.
Point \( P = (3, 12, 5) \). The point on the \( x \)-axis closest to \( P \) is \( A = (3, 0, 0) \).
Step 2: Use the distance formula.
\[ \text{Distance} = \sqrt{(3 - 3)^2 + (12 - 0)^2 + (5 - 0)^2} \] \[ \text{Distance} = \sqrt{0^2 + 12^2 + 5^2} \] \[ \text{Distance} = \sqrt{144 + 25} = \sqrt{169} = 13 \]
Step 1: Identify the projection on the \( x \)-axis.
Point \( P = (3, 12, 5) \). The point on the \( x \)-axis closest to \( P \) is \( A = (3, 0, 0) \).
Step 2: Use the distance formula.
\[ \text{Distance} = \sqrt{(3 - 3)^2 + (12 - 0)^2 + (5 - 0)^2} \] \[ \text{Distance} = \sqrt{0^2 + 12^2 + 5^2} \] \[ \text{Distance} = \sqrt{144 + 25} = \sqrt{169} = 13 \]
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