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

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

Options:

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

Solution:

u × v = |i  j  k| |1  2  3| |4  5  6| = (-3, 6, -3)

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

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

Step 1: Write down the vectors u and v. Here, u = (1, 2, 3) and v = (4, 5, 6).
Step 2: Set up a 3x3 determinant using the unit vectors i, j, k and the components of u and v. It looks like this: |i j k| |1 2 3| |4 5 6|.
Step 3: Calculate the determinant. This involves finding the value of the determinant using the formula: i*(2*6 - 3*5) - j*(1*6 - 3*4) + k*(1*5 - 2*4).
Step 4: Calculate each part: i*(12 - 15) = i*(-3), -j*(6 - 12) = -j*(-6) = j*6, k*(5 - 8) = k*(-3).
Step 5: Combine the results: u × v = (-3, 6, -3).

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