If a bird were to start out from the origin (where the student starts) and fly directly (in a straight line) to the school, what distance db would the bird cover

The question is incomplete! The complete question along with answer and explanation is provided below.

Question:

A student bikes to school by traveling first 1.00 miles north, then 0.500 miles west and finally 0.200 miles south.

If a bird were to start out from the origin (where the student starts) and fly directly (in a straight line) to the school, what distance db would the bird cover

Given Information:  

distance towards north = dn =  1.00 mi

distance towards west = dw =  0.500 mi

distance towards south = ds =  0.200 mi

Required Information:  

distance covered by bird = db = ?

distance covered by bird = 0.94 miles

Explanation:

As you can see in the attached image, by applying the Pythagoras theorem,

db = √(dn - ds)² + dw²

db = √ (1.0 - 0.20)² + 0.50²

db = √ 0.80² + 0.50²

db = 0.94 miles

Therefore, the bird would cover a distance of 0.94 miles

where are the vectors ?

scientific laws are the result of testing theories and proving them to be facts.