Question

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?

Answer 1

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