need help with this question, vectors

Question

A person starts walking from home and walks:

4 miles East

5 miles Southeast

5 miles South

4 miles Southwest

2 miles East

Find the total displacement vector for this walk: ?

Answer 1

4E <4, 0>

5SE <5√2 / 2, -5√2 / 2>

5S <0, -5>

4SW <-2√2, -2√2>

2E <2, 0>

Add x-components and add y-components, That is resulting vector.

Use Pythagoras to determine distance.

Answer 2

Vectors are simply arrows pointing in some direction. A larger quantity is represented with a longer arrow. Vectors add head to tail, so we can either graph them or find their individual x and y coordinates, add them , and then find the magnitude with the pythagorean theroem.

Each vector has an x and a y component:

First: x-direction: 4

y-direction: 0

Second: x-direction: 5*cos(315)

y-direction: 5*sin(315)

Third: x-direction: 0

y-direction: -5

Fourth: x-direction: 4*cos(225)

y-direction: 4*sin(225)

Final: x-direction: 2

y-direction: 0

Next, add all of the x directions together, then all the y directions together. The resulting sums are the components of the resultant vector. This is the displacement vector, and its magnitude is calculated with

|D| = sqroot(xsum^2 + ysum^2)