# Finding the magnitude of b when given the components of c and that the vectors b+c=a

## Homework Statement

If b is added to c = 3.9i + 3.7j, the result is a vector in the positive direction of the y axis, with a magnitude equal to that of c. What is the magnitude of b?

2. The attempt at a solution
I've probably just been staring at these problems for too long...

First of all, is it valid to say the magnitude of a is the sum of the magnitudes of b and c, that is a=b+c ?

Because if so, then c=sqrt(3.9^2+3.7^2)=a

and if a=b+c then b=a-c= 0 ... which is wrong ):

so what should I do?

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supratim1
Gold Member

since b + c is along y axis, so x-component of (b+c) is 0. therefore, tell me what should be the x-component of b?

Welcome to Physics Forums, Emmy!

since b + c is along y axis, so x-component of (b+c) is 0. therefore, tell me what should be the x-component of b?

Welcome to Physics Forums, Emmy!

Thanks so much! (and thanks for replying too :] )

If b+c=0 then bx would have to be -cx, or -3.9?
and then since the y component of b+c equals the y component of c, the y component of b is 0

then you plug in to the equation: magnitude of b= sqrt((-3.9)^2+(0)^2)= 3.9 units?

supratim1
Gold Member

b = -3.9i + Yj (let)

so b + c = (Y + 3.7)j

since magnitudes equal, equate magnitude of c with (Y+3.7), you will find the answer.