The distance of the point P(a,b,c) from the x -axis is.

Engineering

Mathematics

theorem in space

Distance from a Plane

Question

The distance of the point P(a,b,c) from the x -axis is.

$\sqrt{b^{2} + c^{2}}$

$\sqrt{a^{2} + c^{2}}$

$\sqrt{a^{2} + b^{2}}$

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Step 1: Find Co-ordinate of Point on X axis and Find its Distance from Point P

Given:Co-ordinate of Point P=(x1,y1,z1)=(a,b,c)

On X-axis, y and z coordinate will be zero.

∴ Coordinate on the X-axis where perpendicular from point will meet is (x₂,y₂,z₃) = (a,0,0)

By Distance Formula,

Distance Between 2 Points =

\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} + (z_{2} - z_{1})^{2}}

⇒ Distance Between P and X axis

= \sqrt{(a - a)^{2} + (b - 0)^{2} + (c - 0)^{2}}

= \sqrt{b^{2} + c^{2}}

Therefore,Distance Between Point P and X axis is

\sqrt{b^{2} + c^{2}}