Verified answer

let vector B = xi + yj

lets say we call the resultant R

R = B+C = (3+x)i + (4+y)j

since the vector is on the positive y direction it has no x-component (i)

therefore

(3+x)i must be zero, 3+x=0

now we know x = -3

now we can write magnitude of the B vector

|B| = sqrt((-3)^2 + (y)^2)

resultant is actually the y component from the B+C which is = (4+y)j

now the magnitude of the resultant, R is

|R| = sqrt((4+y)^2)

since the B vector and R vector have same magnitude

|B| = |R|

sqrt((-3)^2 + (y)^2) = sqrt((4+y)^2)

now by squaring both sides we get

(-3)^2 + (y)^2 = (4+y)^2

by expandind the RHS and rearranging we get

y = -7/8

using this value now u can replace into |R| or |B| equations above and obtain the magnitude.

its about 3.12