(Simple) Vector Problemdon't see what I'm doing wrong

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The discussion revolves around a vector problem where vector B is added to vector C, resulting in a vector aligned with the positive y-axis and having the same magnitude as C. The magnitude of vector C is calculated as approximately 6.14. The user attempts to find the magnitude of vector B using the Pythagorean theorem but arrives at an incorrect answer of 8.68. Participants suggest clarifying the vector components and re-evaluating the equation setup. The conversation emphasizes the importance of correctly applying vector addition principles to solve the problem.
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(Simple) Vector Problem..don't see what I'm doing wrong!

Homework Statement



If the vector B is added to vector C = 3.7 i + 4.9 j , 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?

Here is what I did -

Magnitude is r = sq rt of Ax^2 + Ay^2 components

therefore, the magnitude of C is

3.7^2 + 4.9^2, take sq rt = 6.14 = magnitude of C

The question is for the magnitude of B. The resultant vector, according to the problem, has the same mag as C, so I would use the Pythagorean theorem =

A^2 + b^2 = C^2

6.14 ^2 + 6.14 ^2 = 75.3992, take sq rt = 8.68.

However this answer is not correct. I do not see where I went wrong, please help. Thank you!
 
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Your question is difficult to follow. From the statement of the problem, start by writing

Bx i + By j + Cx i + Cy j = sqrt[ (Cx)^2 + (Cy)^2 ] j

What's the next step?
 
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