Vectors help please!

[d0minicz]

Hey I'd appreciate any help on this question, my answer for the i value and the j value are the other way around from the book's answer.

Let i be a unit vector in the east direction and j be the unit vector in the north direction. A runner sets off on a bearing of 120 degrees.
a) Find a unit vector in this direction.
b) The runner covers 3 km. Find the position of the runner with respect to her starting point.
c) The runner now turns and runs for 5 km in a northerly direction. Find the position of the runner with respect to her original starting point.
d) Find the distance of the runner from her starting point.

Thanks  !

[TrueTears]

part a)
Let be the unit vector in this direction

since it is a unit vector = 1   Now after u draw a diagram, the angle that the x axis makes with the unit vector is 30 degs, so name this angle

Now

Now is the angle between the unit vector and y axis, which is 60 deg, so  

(negative because its turning clockwise)

Therefore

[Flaming_Arrow]

b.

   


c. 

    


d.

   

[d0minicz]

Thanks alot guys!!!
Damn I used 120 degrees instead of 30 degrees , my bad. Thanks again 

[Flaming_Arrow]

you can use 30 degrees for

[d0minicz]

Hey when TrueTears found a2 in part a), its negative because you have to turn back in the clockwise direction to reach the y-axis right?
Say if it was 75 degrees, would it be positive, since you continue in the anti-clockwise direction to reach the y-axis?

Edit: Can you please draw the bearing for me, I'm getting confused between the x and y-axis. I keep thinking its 120 degrees to its 60 degrees towards the x-axis and 30 degrees back towards the y-axis.

[polky]

Hey when TrueTears found a2 in part a), its negative because you have to turn back in the clockwise direction to reach the y-axis right?
Say if it was 75 degrees, would it be positive, since you continue in the anti-clockwise direction to reach the y-axis?

a2 would be positive because a unit vector with a bearing of 75 degrees would be in the 1st quadrant of a circle, thus both i and j axis values would be positive.  A bearing of 120 degrees would land the vector in the 4th quadrant, where i-direction (a1) is positive and j-direction (a2) is negative.

[d0minicz]

Ahh i get it now... I just cant draw the bearing...I thought it was normal 120 degrees -_-"
Can you help me draw the bearing please, thanks 

Edit: Ah crap forgot a bearing is measured clockwise from North.

[TrueTears]

what i think of it is like, u always go from the vector TO the axis, and if ur turning clockwise then its negative, and if u turn anticlockwise then its positive.

[d0minicz]

Thanks for quick and helpful replies

[kamil9876]

I'm assuming that by AM you mean the vector from A to M. I'll use similair notation as I'm currently lazy with my noob latexing skills.

AM=kAB since the vectors AM and AB are parrelel since AM lies on AB.

hence: |AM|=k|AB|   

Now, |AM|=|AC|
       
So |AC|=k|AB|  (1)

Work out |AC| and |AB| and sub them into equation (1) to find k. Then sub k back into the equation AM=kAB to find AM.