What is the cross product of vectors A = i + j and B = j + k? (2022)

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Question: What is the cross product of vectors A = i + j and B = j + k? (2022)

Options:

Correct Answer: i + k

Solution:

A × B = |i  j  k| |1  1  0| |0  1  1| = i(1*1 - 0*1) - j(1*1 - 0*0) + k(1*0 - 1*0) = i - j.

What is the cross product of vectors A = i + j and B = j + k? (2022)

What is the cross product of vectors A = i + j and B = j + k? (2022)

Step 1: Identify the vectors A and B. A = i + j can be written as (1, 1, 0) and B = j + k can be written as (0, 1, 1).
Step 2: Set up the determinant for the cross product using the unit vectors i, j, k and the components of A and B.
Step 3: Write the determinant as a 3x3 matrix: | i j k | | 1 1 0 | | 0 1 1 |.
Step 4: Calculate the determinant using the formula for the cross product.
Step 5: For the i component, calculate (1*1 - 0*1) = 1.
Step 6: For the j component, calculate (1*1 - 0*0) = 1, and remember to subtract it, so it becomes -1.
Step 7: For the k component, calculate (1*0 - 1*0) = 0.
Step 8: Combine the results from steps 5, 6, and 7 to get the final result: A × B = i - j.

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