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

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