Finding the Magnitude of B in Vector Addition

[devmgnt]

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(a_x² + a_y²)

The Attempt at a Solution

1. Found the magnitude of C

c = sqrt(c_x² + c_y²) = sqrt(3² + 4²) = 5

2. Added B to C and got this equation

5 = sqrt(a_x² + a_y²) = 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.

 

[CFDFEAGURU]

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

 

[mikelepore]

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.

 

[mikelepore]

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

That's not what the question says.

 

[CFDFEAGURU]

"That's not what the question says."

No, I don't agree.

Thanks
Matt

 

[mikelepore]

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.