The length of the perpendicular drawn from the point P(3, 4, 5) on the y-axis is

Question

Philoid · Accepted Answer

Given: point P(3, 4, 5)

To find: length 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 (3 – 0, 4 – y, 5 – 0) = (3, 4 – y, 5)

Let are two vectors as shown in the figure:

The dot product of perpendicular vectors is always zero

Therefore,

⇒ 3 × 0 + (4 – y) × 1 + 5 × 0 = 0

⇒ 0 + 0 + 4 – y= 0

⇒ y = 4

Hence point D(0, 4, 0)

Distance between point P(3, 4, 5) and D(0, 4, 0) is d

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