Finding the magnitude of vector B added to C = 3.0i + 4.0j

[Kp0684]

If B is added to C= 3.0i + 4.0j, 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?... Solution, i got Rx= Ax+Bx+Cx , = (3.0i) and, Ry= Ay+By+Cy, = (4.0j)

So, the square root of (3.0)2 + (4.0)2 = ... (5)...for the magnitude of B... iam i headed in the right direction or am i completely off...

 

[Galileo]

You are given that the direction of the resultant is in the positive y-direction.
So R has the form: $\vec R=A\vec j$. For some A.

 

[HallsofIvy]

Okay: B+ C= R where C= 3 i+ 4 j (which has magnitude 5). You are told that the resultant vector, R, "is a vector in the positive direction of the y-axis, with a magnitude equal to that of C". You then write that "Rx= Ax+Bx+Cx , = (3.0i) and, Ry= Ay+By+Cy, = (4.0j)" which I don't understand at all. Presumably Bx and Cx are x components of B and C, but what is A?

The vector in the positive direction of the y-axis with magnitude 5 (that of C) is
5j. Your equation is B+ 3i+ 4j= 5j. All you have to do to find B is subtract 3i+ 4j from both sides of the equation.