Write the length

Given: point P(3, 5, 12)

To find: length of the perpendicular drawn from the point P from the x-axis

Formula used:

The distance between any two points (a, b, c) and (m, n, o) is given by,

As, y and z coordinate on x-axis are zero

Let point D on x-axis is (x, 0, 0)

Direction cosines of z-axis are (1, 0, 0)

Direction cosines of PD are (3 – x, 5 – 0, 12 – 0) = (3 – x, 5, 12)

Let are two vectors as shown in the figure:

The dot product of perpendicular vectors is always zero

Therefore,

⇒ (3 – x) × 1 + 5 × 0 + 12 × 0 = 0

⇒ 3 – x + 0 + 0 = 0

⇒ x = 3

Hence point D(3, 0, 0)

Distance between point P(3, 5, 12) and D(3, 0, 0) is d

= 13

Hence, the distance of the point P from x-axis is 13 units