The distance of a point \( P(a, b, c) \) from the y-axis is the perpendicular distance from \( P \) to the y-axis.
The y-axis corresponds to the line where \( x = 0 \) and \( z = 0 \).
The perpendicular distance is: \[ \text{Distance} = \sqrt{(a - 0)^2 + (c - 0)^2} = \sqrt{a^2 + c^2}. \]
Therefore, the correct answer is (C) \( \sqrt{a^2 + c^2} \).
Determine whether each of the following relations are reflexive, symmetric, and transitive.
Show that the relation R in the set R of real numbers, defined as
R = {(a, b): a ≤ b2 } is neither reflexive nor symmetric nor transitive.
Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as
R = {(a, b): b = a + 1} is reflexive, symmetric or transitive.
Assertion (A): A line in space cannot be drawn perpendicular to \( x \), \( y \), and \( z \) axes simultaneously.
Reason (R): For any line making angles \( \alpha, \beta, \gamma \) with the positive directions of \( x \), \( y \), and \( z \) axes respectively, \[ \cos^2\alpha + \cos^2\beta + \cos^2\gamma = 1. \]