)⊤ The Lorentz force is calculated using the formula: F=q(E+v×B) First, solve for v×B : v×B‌=|
∧
i
∧
j
∧
k
2
3
0
0
2
3
| ‌=(9
∧
i
−6
∧
j
+4
∧
k
) Now, find the total force F : F‌=q[(3
∧
i
+6
∧
j
+2
∧
k
)+(9
∧
i
−6
∧
j
+4
∧
k
)] ‌=q[12
∧
i
+6
∧
k
] For an electron, q=1.6×10−19C : F‌=1.6×10−19×[12
∧
i
+6
∧
k
] |F|‌=1.6×10−19×√122+62 |F|‌=1.6×10−19×√180 |F|‌=2.15×10−18N To determine the direction of F with respect to the X-axis: θ=tan−1(‌