# Vector and magnitude problem

## Homework Statement

A little assistance with this question:-

A vector, B, when added to the vector C = 3i + 4j yields a resultant vector which is in the positive y direction and has a magnitude equal to that of C. What is the magnitude of B?

## The Attempt at a Solution

i found the magnitude of C to be 5 i.e.

sqrt(3^2 + 4^2)= 5

since the question says this magnitude is equal to that of the resultant vector and taking the unit vector of B to be (x)i + (y)j; i equated it to 5 so i can try to solve for x and y i.e

(x+3)i + (y+4)j = 5

this is where i got stuck..

please any help will be very appreciated .. thanks

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rock.freak667
Homework Helper
So the vector B added to C is B+A=(x+3)i + (y+4)j

if the (B+A) points in the positive y-direction, then what should 'x' be?

When you get that, then apply |B+A| = |C|

i think x would be zero right??? if dat's right what wuld y be??
Also ur notation is a bit confusing.. what is the vector A?? Also the vector in the positive y direction is supposed to be the resultant vector i.e B + C BUT u wrote B + A..i'm kinda confused there..

rock.freak667
Homework Helper
i think x would be zero right??? if dat's right what wuld y be??
Also ur notation is a bit confusing.. what is the vector A?? Also the vector in the positive y direction is supposed to be the resultant vector i.e B + C BUT u wrote B + A..i'm kinda confused there..
Sorry, I meant to type 'C', replace 'A' with 'C' is all.

you would have (x+3) being zero.