Q. 25.0( 2 Votes )

Write the distance of the point P(3, 4, 5) from the z-axis.

Answer :

Given: point P(3, 4, 5)


To find: distance of the point P from the z-axis


Formula used:


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



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


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


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


Direction cosines of PD are (3 – 0, 4 – 0, 5 – z) = (3, 4, 5 – z)


Let are two vectors as shown in the figure:



The dot product of perpendicular vectors is always zero


Therefore,


3 × 0 + 4 × 0 + (5 – z) × 1 = 0


0 + 0 + 5 – z = 0


z = 5


Hence point D(0, 0, 5)


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






= 5


Hence, the distance of the point P from z-axis is 5 units


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