Question

The distance of the plane whose equation is given by 3x − 4y + 12z = 3, from the origin will be ______.

Options

• `3/13`

• `(−2)/13`

• −3

• `13/19`

Answer 1

The distance of the plane whose equation is given by 3x − 4y + 12z = 3, from the origin will be `bbunderline(3/13)`.

Explanation:

Given:

Eqn. of plane = 3x − 4y + 12z = 3

∵ d = `|ax_0 + by_0 + cz_0 + d|/sqrt(a^2 + b^2 + c^2)`

(x₀, y₀, z₀) = (0, 0, 0,)              ...[·: Origin]

and a = 3, b = −4, c = 12, d = −3

∴ d = `|0 + 0 + 0 −3|/sqrt(9 + 16 + 144) = 3/13`

Option `3/13` is correct.