alleryFor vectors ā = î - ĵ + 2k̂ and b̄ = 3î + 2ĵ - k̂, find the AREA of the parallelogram formed (use |ā × b̄|):
A√110
B√83
C√50
D√70
Answer & Solution
Correct answer: B. √83
ā × b̄ via determinant: i: (-1)(-1) - (2)(2) = 1 - 4 = -3. j: -[(1)(-1) - (2)(3)] = -(-1 - 6) = 7. k: (1)(2) - (-1)(3) = 2 + 3 = 5. So ā × b̄ = -3î + 7ĵ + 5k̂.
|ā × b̄| = √(9 + 49 + 25) = √83. Area of parallelogram = √83.
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