Question

Vector addition?? Please see below!

You are given vector a= <3, 5>, with a magnitude of √34cm and direction of 59o and vector b= <-4, 3> with a magnitude of 5cm and a direction of 143.1o.

a) Find the resultant (sum) by hand (magnitude and direction) by sketching (use the triangle method). See the video for directions on this. Show all markings and label everything.
b) Find the resultant (sum) by using vector addition. Show work.
c) Write 1-2 sentences about how these provide the same answer despite looking very different.

Answer 1

See below.

Explanation:

a.) You can see on the diagram that this has a displacement of

`((-1),(8))`. The magnitude from diagram can be found using

Pythagoras's theorem, where `a+b` is the hypotenuse.

`sqrt((-1)^2+(8)^2)=sqrt(65)`

b.)

`a = ((3),(5))` , `b=((-4),(3))`

Resultant vector `a+b`

`a+b= ((3),(5)) +((-4),(3))=((3+(-1)),(5+3))=((-1),(8))`

The direction of `a+b` is found by using the ratio `8/-1`

`tan^(-1) (8/-1)=- 82.9^o`

( this is the angle between `a+b` and the negative x axis measured in a clockwise direction)

c.) You will have to do this part, by looking at your text book.