Question

A person moves towards East for 3 m, then towards North
for 4 m and then moves vertically up by 5 m. What is his
distance now from the starting point?​

Answer 1

Answer:

$5\sqrt{2}$ m

Explanation:

Consider a three dimensional rectangular coordinate system.

Let the initial position of the person be the origin O with coordinates (0,0,0).

Let the positive x- axis and the negative x-axis represent East and West directions respectively.

Let the positive y-axis and the negative y-axis represent the North and the South respectively.

Let the vertically upward direction be along the positive z-axis.

Let P be the point representing the final position of the person.

According to the data in the given question, the coordinates of the final position P are (3,4,5).

Distance from the starting point =  Length of OP

                                                     = $\sqrt(3^{2}+4^{2}+5^{2})$ m

                                                     = $\sqrt{50}$ m

                                                     = $5\sqrt{2}$ m