Finding the magnitude of a vector B given vector C

[Cadawallader]

Homework Statement

If vector B is added to vector C = 3.7i + 2.4j, the result is a vector in the positive direction of the y axis, with a magnitude equal to that of vector C. What is the magnitude of vector B?

Homework Equations

sqroot(a^2x+a^2y) = a

The Attempt at a Solution

My line of reasoning: since the magnitude of vector B is equal to the magnitude of vector C, then finding the magnitude of vector C using the given components would yield the magnitude of vector B.

How I went about solving the problem:

I used 3.7i as the x component of C and 2.4j as the Y component, then plugged each component into the following formula: c = sqroot(c²x+c²y). I received an answer of 4.4 but it has been marked as incorrect.

Please let me know why my reasoning is incorrect (I don't need the answer).

 

[BvU]

Hello Cada, welcome to PF !

Did you make a drawing of the situation ?

 

[Cadawallader]

Hello Cada, welcome to PF !

Did you make a drawing of the situation ?

Hi,

Thanks for replying. No, I had not created an illustration of the situation at the time since I did not believe it would be necessary for this question.

I created one just now but I still do not see how it will help yield the magnitude of vector C.

Here is the drawing: http://i60.tinypic.com/2zrf6og.jpg

 

[Chestermiller]

If the x component of the resultant is equal to zero, what does the x component of B have to be?

Chet

 

[Cadawallader]

Hello,

Apologies.. I am reading the question incorrectly therefore assuming that the magnitude of vector B is equal to that of vector C when this is not the case.

I will give this another go - thank you for suggesting to draw this and helping.

 

[BvU]

Dear Cad,

In the picture it is hard to imagine you made the magnitude of $\vec a$ equal to the magnitude of $\vec c$. -- Ah, you've got it! See that making a picture helps out ?