You are going for a drive, but a detour takes you out of the way of your destination. You
drive north for 10 miles, turn right and drive east for 5 miles, turn to the north and drive for 3
miles, drive west for 10 miles, and arrive at your destination.
a) How far from where you started did you end up?
b) If you wanted to travel directly to your destination without following the streets (“as the
crow flies”), what angle would you take? What direction would a compass read?
c) Now try adding the vectors in a different order. For example, start with the 5 miles east,
then 3 miles north, etc., as long as you add all four vectors. Compare the result to the sum
in part a). Draw the vectors in the order you used.

You drive north for 10 miles, turn right and drive east for 5 miles, turn to the north and drive for 3 miles, drive west for 10 miles, and arrive at your destination.

According to diagram

(a).We need to calculate the distance

Using pythagorean theorem

[tex]EO=\sqrt{(ED)^2+(DO)^2}[/tex]

Put the value into the formula

[tex]EO=\sqrt{5^2+(13)^2}[/tex]

[tex]EO=13.92\ miles[/tex]

(b). We need to calculate the direction

Using formula of direction

[tex]\theta=\tan^{-1}(\dfrac{OD}{DE})[/tex]

Put the value into the formula

[tex]\theta=\tan^{-1}(\dfrac{13}{5})[/tex]

[tex]\theta=68.9^{\circ}[/tex]

The direction is 68.9° north - west.

(c). We need to draw a vector diagram

According to vector diagram,

The distance between started point and end point will be same.

Hence, (a). The distance between started point and end point is 13.92 miles.

(b), The direction is 68.9° north - west.