How to Solve Vector Problems in Rotated Coordinate Systems

[iconwin]

I found the answer for the first part of the problem to be 10 units. But I have no clue how to deal with the second part :) Please give some hints how to solve this following prob.

Homework Statement

Two vector A and B, are drawn on an x-y coordinate system as shown. Vector A has a magnitude of 8 units, and vector B has a magnitude of 6 units. Find the x- and the y- components of vector A and B in the x-y system. Compute the magnitude of the resultant in the x-y coordinate system. A second coordinate system, the x'-y' system , is rotated 37 degree with respect to the x-y system as shown. Find the x'- and y'- components of A and B in the x'-y' system. Compute the magnitude of the resultant vector in the x'-y' coordinate system.

Homework Equations

no clue :(

The Attempt at a Solution

Don't know!

 

[LowlyPion]

I found the answer for the first part of the problem to be 10 units. But I have no clue how to deal with the second part :) Please give some hints how to solve this following prob.

Homework Statement

Two vector A and B, are drawn on an x-y coordinate system as shown. Vector A has a magnitude of 8 units, and vector B has a magnitude of 6 units. Find the x- and the y- components of vector A and B in the x-y system. Compute the magnitude of the resultant in the x-y coordinate system. A second coordinate system, the x'-y' system , is rotated 37 degree with respect to the x-y system as shown. Find the x'- and y'- components of A and B in the x'-y' system. Compute the magnitude of the resultant vector in the x'-y' coordinate system.

Homework Equations

no clue :(

The Attempt at a Solution

Don't know!

You have the magnitude, but how would you write the vectors in the x-y?

For instance A = 8 * x-hat + 0 * y-hat
Now write B.

For the x'-y' translation you simply state these vectors in their components at the appropriate angles to the new axes.

 

[iconwin]

Aha ;)) Great thank to you! I'll try it now.

 

[iconwin]

So, I have the result:

Ax'= 8cos37x'-hat= (6.4x'-hat)
Ay'= -8sin37y'-hat = -4.8y'-hat

Bx'= 6cos37x'-hat= 4.8x'-hat
By'= 6sin37y'-hat = 3.6y'-hat

Is it right?

 

[LowlyPion]

So, I have the result:

Ax'= 8cos37x'-hat= (6.4x'-hat)
Ay'= -8sin37y'-hat = -4.8y'-hat

Bx'= 6cos37x'-hat= 4.8x'-hat
By'= 6sin37y'-hat = 3.6y'-hat

Is it right?

That looks right. I would express it as the sum of the x and y components though.

 

[iconwin]

;)) Thanks a lot, LowlyPion for your helpfulness and kindness.