Given vectors A = 4i + 3j and B = 1i + 2j, calculate A · B.

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Question: Given vectors A = 4i + 3j and B = 1i + 2j, calculate A · B.

Options:

Correct Answer: 10

Solution:

A · B = (4)(1) + (3)(2) = 4 + 6 = 10.

Given vectors A = 4i + 3j and B = 1i + 2j, calculate A · B.

Given vectors A = 4i + 3j and B = 1i + 2j, calculate A · B.

Step 1: Identify the components of vector A. A = 4i + 3j means A has a component of 4 in the i direction and 3 in the j direction.
Step 2: Identify the components of vector B. B = 1i + 2j means B has a component of 1 in the i direction and 2 in the j direction.
Step 3: Multiply the i components of A and B together. This is (4)(1) = 4.
Step 4: Multiply the j components of A and B together. This is (3)(2) = 6.
Step 5: Add the results from Step 3 and Step 4 together. This is 4 + 6 = 10.
Step 6: The final result of A · B is 10.

Dot Product – The dot product of two vectors is calculated by multiplying their corresponding components and summing the results.
Vector Components – Understanding how to break down vectors into their i and j components is essential for performing vector operations.