If Upper B Overscript right-arrow EndScripts is added to Upper C Overscript right-arrow EndScripts equals 7.1 i Overscript ̂ EndScripts plus 3.1 j Overscript ̂ EndScripts, the result is a vector in the positive direction of the y axis, with a magnitude equal to that of Upper C Overscript right-arrow EndScripts. What is the magnitude of Upper B Overscript right-arrow EndScripts?
call unknown vector U
U = 0 i + |C| j
= [bx+cx] i + [by+cy]j
|C| = sqrt(7.1^2+3.1^2)
so
bx + cx = ux = 0
bx = -cx = -7.1
and
by + 3.1 = uy = |C|
so
by = |C| - 3.1
B = bx i + by Jj
To determine the magnitude of Upper B, we need to solve the equation by isolating the magnitude of Upper B Overscript right-arrow EndScripts. Here's how we can do that:
1. Start with the given equation: Upper B Overscript right-arrow EndScripts + Upper C Overscript right-arrow EndScripts = 7.1 i Overscript ̂ EndScripts + 3.1 j Overscript ̂ EndScripts.
2. Since we know that the result is a vector in the positive direction of the y-axis, we can write the equation as: Upper C Overscript right-arrow EndScripts = 0 i Overscript ̂ EndScripts + Upper B Overscript right-arrow EndScripts.
3. Now we can equate the corresponding components of the vectors:
0 i Overscript ̂ EndScripts + Upper B Overscript right-arrow EndScripts = 7.1 i Overscript ̂ EndScripts + 3.1 j Overscript ̂ EndScripts.
4. Focus on the y-component of the equation: Upper B Overscript right-arrow EndScripts + 0 = 3.1.
5. Simplify: Upper B Overscript right-arrow EndScripts = 3.1.
Therefore, the magnitude of Upper B Overscript right-arrow EndScripts is 3.1.