Question

David walks 3 km north, and then turns east and walks 4 km. What is the distance?

Answer 1

Answer:

7 km is the distance

Explanation:

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Answer 2

$\huge\pink{ANSWER}$

Using i and j as the unit vectors in the x- and y-directions, and taking east to be the x-direction, then the boy’s final position is

r = 4i + 3j

The magnitude of this vector is √(4^2 + 3^2) = 5

The angle of the boy is Tan^-1(4/3) = 53.13° east of north

So the boy’s final position is 5km from the starting point, 53.13° east of north.

Of course, we all recognized that it was a 3–4–5 triangle, but I used the vector approach (which is the correct approach) to demonstrate the method.

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