74. Letting B
x
= B
y
= B
1
and B
z
= B
2
and using Eq. 29-2 and Eq. 3-30, we obtain (with SI units
understood)
F
=
q
v
×
B
4ˆi
− 20ˆj+ 12ˆk = 2
(4B
2
− 6B
1
)ˆi + (6B
1
− 2B
2
)ˆj + (2B
1
− 4B
1
) ˆ
k
.
Equating like components, we find B
1
=
−3 and B
2
=
−4. In summary (with the unit Tesla understood),
B =
−3.0ˆi− 3.0ˆj− 4.0ˆk.