What is the cross product of vectors A = i + 2j and B = 3i + 4j? (2021)

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Question: What is the cross product of vectors A = i + 2j and B = 3i + 4j? (2021)

Options:

Correct Answer: -2k

Exam Year: 2021

Solution:

A × B = |i  j  k| |1  2  0| |3  4  0| = (0 - 0)i - (0 - 0)j + (4 - 6)k = -2k.

What is the cross product of vectors A = i + 2j and B = 3i + 4j? (2021)

What is the cross product of vectors A = i + 2j and B = 3i + 4j? (2021)

Step 1: Identify the vectors A and B. A = i + 2j can be written as (1, 2, 0) and B = 3i + 4j can be written as (3, 4, 0).
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 2 0| |3 4 0|.
Step 4: Calculate the determinant. Start with the first row: i component = (2*0 - 0*4) = 0.
Step 5: Calculate the j component: j component = -(1*0 - 0*3) = 0.
Step 6: Calculate the k component: k component = (1*4 - 2*3) = 4 - 6 = -2.
Step 7: Combine the components to get the final result: A × B = 0i - 0j - 2k = -2k.

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