Given vectors A = i + 2j and B = 3i + 4j, calculate A · B. (2022)

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Question: Given vectors A = i + 2j and B = 3i + 4j, calculate A · B. (2022)

Options:

Correct Answer: 11

Exam Year: 2022

Solution:

A · B = (1)(3) + (2)(4) = 3 + 8 = 11.

Given vectors A = i + 2j and B = 3i + 4j, calculate A · B. (2022)

Given vectors A = i + 2j and B = 3i + 4j, calculate A · B. (2022)

Step 1: Identify the components of vector A. A = i + 2j means A has a component of 1 in the i direction and 2 in the j direction.
Step 2: Identify the components of vector B. B = 3i + 4j means B has a component of 3 in the i direction and 4 in the j direction.
Step 3: Multiply the i components of A and B. This is (1)(3) = 3.
Step 4: Multiply the j components of A and B. This is (2)(4) = 8.
Step 5: Add the results from Step 3 and Step 4. This is 3 + 8 = 11.
Step 6: The final result of A · B is 11.

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.