In the cross (or vector) product Upper F Overscript right-arrow EndScripts equal
ID: 1869528 • Letter: I
Question
In the cross (or vector) product Upper F Overscript right-arrow EndScripts equals q v Overscript right-arrow EndScripts times Upper B Overscript right-arrow EndScripts we know that q equals 1 Upper F Overscript right-arrow EndScripts equals -55 i Overscript EndScripts plus -36 j Overscript EndScripts plus -26 k Overscript EndScripts v Overscript right-arrow EndScripts equals negative 6.0 i Overscript EndScripts plus 7.0 j Overscript EndScripts plus 3.0 k Overscript EndScripts Upper B Overscript right-arrow EndScripts equals Upper B Subscript x Baseline i Overscript EndScripts plus Upper B Subscript y Baseline j Overscript EndScripts plus Upper B Subscript z Baseline k Overscript EndScripts What then is Upper B Overscript right-arrow EndScripts in unit-vector notation if Bx = By?
Explanation / Answer
given
F = qv * B
q = 1
F = -55i - 36 j - 26 k
v = -6i + 7j + 3k
B = Bxi + Byj + Bzk
now,
(-55i - 36 j - 26 k) = (-6i + 7j + 3k) x (Bxi + Byj + Bzk)
(-55i - 36 j - 26 k) = -6Byk + 6Bzj - 7Bxk + 7Bzi + 3Bxj - 3Byi
comparing
-6By - 7Bx = -26
6Bz + 3Bx = -36
7Bz - 3By = -55
for Bx = By
Bx = By = 2
Bz = -7