alleryFind ā × b̄ where ā = î + 2ĵ + k̂ and b̄ = 2î + ĵ + 3k̂:
Aî + ĵ + k̂
B5î - ĵ + 5k̂
C5î - ĵ - 3k̂
D5î - 5ĵ - 5k̂
Answer & Solution
Correct answer: C. 5î - ĵ - 3k̂
**Use determinant:** ā × b̄ = |î ĵ k̂; 1 2 1; 2 1 3|.
i: 2(3)-1(1) = 6-1 = 5 (positive).
j: -(1×3 - 1×2) = -(3-2) = -1 (so coefficient -1).
k: 1(1)-2(2) = 1-4 = -3 (so coefficient -3). Result: 5î - ĵ - 3k̂.
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