Finding the Magnitude of B in Vector Addition

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To find the magnitude of vector B in the equation B + C = R, where C = 3.0î + 4.0ĵ and R is directed positively along the y-axis with the same magnitude as C, it is essential to first determine the magnitude of C, which is 5. The equation simplifies to B = R - C, and since R has no x-component, B must counteract C's x-component. The discussion highlights that the magnitude of B must be an irrational number, derived from the vector arithmetic involving C and R. Ultimately, the correct approach involves understanding the relationship between the components of the vectors rather than solely focusing on their magnitudes.
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Homework Statement



If B is added to C = 3.0î + 4.0ĵ, 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?


Homework Equations



a = sqrt(ax2 + ay2)



The Attempt at a Solution



1. Found the magnitude of C

c = sqrt(cx2 + cy2) = sqrt(32 + 42) = 5

2. Added B to C and got this equation

5 = sqrt(ax2 + ay2) = sqrt(b2 + 52)

which obviously isn't right because I get the magnitude of B as 0. I'm not sure what I am doing wrong, but any guidance would be helpful. Thank you.
 
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Think it through.

The equation you are trying to solve is;

B+C=C

In words "the magnitude of B plus the magnitude of C equals the magnitude of C"

You don't even need to find their magnitudes.

Make sense yet?

Thanks
Matt
 
If B + C = result R, then B = R - C. Convert the phrase "the result is a vector in the positive direction of the y axis, with a magnitude equal to that of C" into a components and a unit vector, and then subtract C from it, vector arithmetic. They're asking you for the magnitude of that last one.
 
CFDFEAGURU said:
In words "the magnitude of B plus the magnitude of C equals the magnitude of C"

That's not what the question says.
 
"That's not what the question says."

No, I don't agree.

Thanks
Matt
 
C and "the result" R have the same magnitudes, and yet C has two positive components, while R is entirely in the +y direction. What are you going to add to C to get R? Hint: Its magnitude will be an irrational number that has to be rounded off according to the number of significant digits in the given components of C.
 
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