What is the cross product of vectors (1, 2, 3) and (4, 5, 6)?

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Question: What is the cross product of vectors (1, 2, 3) and (4, 5, 6)?

Options:

Correct Answer: (-3, 6, -3)

Solution:

Cross product = |i  j  k| |1  2  3| |4  5  6| = (-3, 6, -3)

What is the cross product of vectors (1, 2, 3) and (4, 5, 6)?

What is the cross product of vectors (1, 2, 3) and (4, 5, 6)?

Step 1: Write down the vectors. We have vector A = (1, 2, 3) and vector B = (4, 5, 6).
Step 2: Set up the determinant using the unit vectors i, j, k. This looks like: |i j k| |1 2 3| |4 5 6|.
Step 3: Expand the determinant. This means we will calculate it using the formula: i*(2*6 - 3*5) - j*(1*6 - 3*4) + k*(1*5 - 2*4).
Step 4: Calculate each part: For i, we get 2*6 - 3*5 = 12 - 15 = -3. For j, we get 1*6 - 3*4 = 6 - 12 = -6, but we subtract this, so it becomes +6. For k, we get 1*5 - 2*4 = 5 - 8 = -3.
Step 5: Combine the results. The cross product is (-3, 6, -3).

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