What is the dot product of vectors A = 2i + 3j and B = 4i - j? (2022)

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Question: What is the dot product of vectors A = 2i + 3j and B = 4i - j? (2022)

Options:

Correct Answer: 10

Solution:

A · B = (2)(4) + (3)(-1) = 8 - 3 = 5.

What is the dot product of vectors A = 2i + 3j and B = 4i - j? (2022)

What is the dot product of vectors A = 2i + 3j and B = 4i - j? (2022)

Step 1: Identify the components of vector A. A = 2i + 3j means A has a component of 2 in the i direction and 3 in the j direction.
Step 2: Identify the components of vector B. B = 4i - j means B has a component of 4 in the i direction and -1 in the j direction.
Step 3: Multiply the i components of A and B together. This is (2)(4) = 8.
Step 4: Multiply the j components of A and B together. This is (3)(-1) = -3.
Step 5: Add the results from Step 3 and Step 4 together. This is 8 + (-3) = 8 - 3 = 5.
Step 6: The final result is the dot product of vectors A and B, which is 5.

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