If the vector a = (3, 4) and b = (1, 2), find the cross product a × b.

If the vector a = (3, 4) and b = (1, 2), find the cross product a × b.

Correct Answer: 2

Step 1: Identify the components of vector a. Here, a = (3, 4) means a1 = 3 and a2 = 4.
Step 2: Identify the components of vector b. Here, b = (1, 2) means b1 = 1 and b2 = 2.
Step 3: Use the formula for the cross product in 2D, which is a × b = a1 * b2 - a2 * b1.
Step 4: Substitute the values into the formula: a × b = 3 * 2 - 4 * 1.
Step 5: Calculate 3 * 2, which equals 6.
Step 6: Calculate 4 * 1, which equals 4.
Step 7: Subtract the second result from the first: 6 - 4 = 2.
Step 8: The final result of the cross product a × b is 2.

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