Question

Find the magnitude and direction of the vector. Round the length to the nearest tenth and the degree to the nearest unit. The diagram is not drawn to scale.

Could I have each step of this so I know what to do on other questions like this?

Answer 1

a^2 + b^2 = c^2

6^2 + 4^2 = c^2

...
...
...

c = ??

Answer 2

Solving for c will give you the magnitude or length of the vector

Answer 3

Pythagorean Theorem? I did not know to use that 0.0 THANK you!!!

Answer 4

you're welcome

Answer 5

and yes the pythagorean theorem is useful for calculating lengths (with right triangles) and finding distances between two points

Answer 6

to find the direction of the vector, you just need to find this angle here

Answer 7

let's call this angle theta (symbol is a 0 with a horizontal line through it)

Answer 8

it turns out that

tangent(angle) = opposite/adjacent

tan(theta) = 4/6

tan(theta) = 2/3

theta = arctan(2/3)

theta = 33.6900675 degrees (use a calculator here)

Note: make sure you're in degree mode

Answer 9

oh and almost forgot

Answer 10

the fact that they added on north, east, south, west means the direction is really

33.6900675 degrees north of east

ie you start looking directly east, then you turn north roughly 33.6900675 degrees to arrive at the direction you want to look at