Vector Magnitude problem?

Question

While vacationing in the mountains you do some hiking. In the morning, your displacement is (2500 , east) + (4000 north) + (200 , vertical). After lunch, your displacement is (1600 , west) + (2700 , north) - (500 , vertical).

What is the total magnitude of your displacement for the day?

Answer 1

east is in +x, west is -x

north and south are +y, -y respectfully

north is on +z and south is on -z

then <2500, 4000, 200> + <-1600, 2700, -500> = <4100, 6700, -300>

or 4100 east, 6700 north and 300 down

magnitude is = to sqrt(4100^2 + 6700^2 - 300^2) = about 4165