For vectors A = 6i + 8j and B = 2i + 3j, find A · B.

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Question: For vectors A = 6i + 8j and B = 2i + 3j, find A · B.

Options:

Correct Answer: 42

Solution:

A · B = (6)(2) + (8)(3) = 12 + 24 = 36.

For vectors A = 6i + 8j and B = 2i + 3j, find A · B.

For vectors A = 6i + 8j and B = 2i + 3j, find A · B.

Step 1: Identify the components of vector A, which are 6 (i component) and 8 (j component).
Step 2: Identify the components of vector B, which are 2 (i component) and 3 (j component).
Step 3: Multiply the i components of A and B together: 6 (from A) * 2 (from B) = 12.
Step 4: Multiply the j components of A and B together: 8 (from A) * 3 (from B) = 24.
Step 5: Add the results from Step 3 and Step 4 together: 12 + 24 = 36.
Step 6: The final result of A · B is 36.

Dot Product of Vectors – The dot product of two vectors A and B is calculated by multiplying their corresponding components and summing the results.