Question

The distance of the point (10, 10, 10) from the Z-axis.

Hint:

Remember: The distance of a point from the Z-axis is calculated using only the \(x\) and \(y\) coordinates of the point.

Answer 1

Step 1: Use the distance formula from a point to the Z-axis.
The Z-axis has coordinates (0, 0, z). The distance \(d\) from a point \((x_1, y_1, z_1)\) to the Z-axis is given by the formula: \[ d = \sqrt{x_1^2 + y_1^2} \]
Step 2: Apply the formula to the given point (10, 10, 10).
Substitute \(x_1 = 10\) and \(y_1 = 10\): \[ d = \sqrt{10^2 + 10^2} = \sqrt{100 + 100} = \sqrt{200} = 10\sqrt{2} \] Thus, the distance of the point (10, 10, 10) from the Z-axis is: \[ \boxed{10\sqrt{2}} \]