Given: point P(1, 2, 3)

To find: coordinates of the foot of the perpendicular from the point on the y-axis

Formula used:

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

As x and z coordinate on the y-axis is zero

Let point D is the point of the foot of perpendicular on the y-axis from point P be (0, y, 0)

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

Direction cosines of PD are (1 – 0, 2 – y, 3 – 0) = (1, 2 – y, 3)

Let are two vectors as shown in the figure:

The dot product of perpendicular vectors is always zero

Therefore,

⇒ 1 × 0 + (2 – y) × 1 + 3 × 0 = 0

⇒ 0 + 0 + 2 – y= 0

⇒ y = 2

Hence, coordinates of point D are (0, 2, 0)