What is the cross product of the vectors (1, 0, 0) and (0, 1, 0)?

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Question: What is the cross product of the vectors (1, 0, 0) and (0, 1, 0)?

Options:

Correct Answer: (0, 0, 1)

Solution:

Cross product = (1, 0, 0) × (0, 1, 0) = (0, 0, 1).

What is the cross product of the vectors (1, 0, 0) and (0, 1, 0)?

What is the cross product of the vectors (1, 0, 0) and (0, 1, 0)?

Step 1: Identify the two vectors. The first vector is (1, 0, 0) and the second vector is (0, 1, 0).
Step 2: Write down the formula for the cross product of two vectors A = (a1, a2, a3) and B = (b1, b2, b3). The formula is: A × B = (a2*b3 - a3*b2, a3*b1 - a1*b3, a1*b2 - a2*b1).
Step 3: Substitute the values from the vectors into the formula. Here, A = (1, 0, 0) and B = (0, 1, 0). So, a1 = 1, a2 = 0, a3 = 0, b1 = 0, b2 = 1, b3 = 0.
Step 4: Calculate each component of the cross product using the formula.
Component 1: a2*b3 - a3*b2 = 0*0 - 0*1 = 0.
Component 2: a3*b1 - a1*b3 = 0*0 - 1*0 = 0.
Component 3: a1*b2 - a2*b1 = 1*1 - 0*0 = 1.
Step 5: Combine the components to get the final result. The cross product is (0, 0, 1).

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