Trig and Vector Components

[iamhumble]

Hi -

The problem is below and picture of diagram is attached. Could you tell me what is incorrect about my train of thought? I am suppose to express x and y.

Find the components of the vector with length
C and angle phi as shown, named C vector. Express your answer in terms of C and phi . Write the components in the form (x,y) .

I expressed (x,y) as ... c*cos(phi),c*csc(phi) ... which is incorrect

Thanks for your time.

[robphy]

The component of any vector \vec V along a given axis is
V_{axis}=|V|\cos \theta_{\rm between\ \vec V\ and\ axis}

In your picture, what is \theta_{\rm between\ \vec V\ and\ x-axis} and \theta_{\rm between\ \vec V\ and\ y-axis} ?
With the trig identity for \cos(\phi+\alpha), you can express all of your results in terms of \phi.

[needhelpperson]

Hi -

The problem is below and picture of diagram is attached. Could you tell me what is incorrect about my train of thought? I am suppose to express x and y.

Find the components of the vector with length
C and angle phi as shown, named C vector. Express your answer in terms of C and phi . Write the components in the form (x,y) .

I expressed (x,y) as ... c*cos(phi),c*csc(phi) ... which is incorrect

Thanks for your time.

I'm just wondering, can't you express the answer as
c*sin(phi),c*cos(phi) ?

correct me if im wrong...

[robphy]

Almost... note that c_x < 0.

[needhelpperson]

Almost... note that c_x < 0.

thanks alot, i was just confused because iamhumble made it seem a lot harder...

[Electro]

Hello Everyone,
In school I had a test of Vector exercises. The problem is that I have to submit them online and I need the exact value for the questions. Anyway I don't want you to solve them for me. I just need some help where I am stuck.

The first exercise: A boy runs 3.3 m North, 7.1 m NorthEast and 15.6 m West. a)Determine the length of the displacement vector tha goes from the starting point to his final position. b)Determine the direction of the displacement vector.

I was confused by this exercise because there isn't any angle given. So I assumed that "NorthEast" means that he moves 7.1 m with an angle 45 Deg.
Then part a) is easy. For part b) I found the angle formed by the North line and the Resultant vector. Am I right here?

The next exercise is a little fuzzy I think: Let aA + bB + C=0, where
A=(17,-99), B=(-99,28) and C=(4.3,78), where Ax=17 units, Ay=-99 units etc. What is the value of a and b? (All the Upper case letters A,B and C have the vector arrow above).
What I did is: I opened aA + bB + C=0 using unit vectors i, j and k (k=0) and the numbers given above.
Still I have a and b and it's an equation with 2 unknowns.
The final expression I concluded is: (a*17i-b*99i+4.3i)+(b*28j-a*99j+78j)=0...........???

Thank You for your time.

[Tide]

Electro,

Your final equation is really TWO equations since the unit vectors are independent of each other. You should be able to handle it from there.

[Electro]

:smile: Thank You Tide,
What I think now, is forming two simultaneous equations.
1) 17a-99b= -4.3
2) 28b-99a= -78
Solving them, I think is the answer for a and b.
Since the i units can't be added to the j units I formed two equations just neglecting i and j. So for i group it will give 0 and for j group too.

Please I need an answer on the previous exercise I posted if I have concepted it right or not.

Thank you
Electro

[iamhumble]

Thanks all for the much needed assistance. I understand what I did wrong.

[Electro]

:uhh: Anyone can give the answer to my questions?

[needhelpperson]

i think you should start a new post of your own...