If the vectors A = 1i + 2j and B = 2i + 1j, find A · B. (2023)

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Question: If the vectors A = 1i + 2j and B = 2i + 1j, find A · B. (2023)

Options:

Correct Answer: 5

Exam Year: 2023

Solution:

A · B = (1)(2) + (2)(1) = 2 + 2 = 4

If the vectors A = 1i + 2j and B = 2i + 1j, find A · B. (2023)

If the vectors A = 1i + 2j and B = 2i + 1j, find A · B. (2023)

Step 1: Identify the components of vector A. A = 1i + 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 = 2i + 1j means B has a component of 2 in the i direction and 1 in the j direction.
Step 3: Use the formula for the dot product of two vectors. The dot product A · B is calculated as (A's i component) * (B's i component) + (A's j component) * (B's j component).
Step 4: Substitute the values into the formula. A · B = (1) * (2) + (2) * (1).
Step 5: Calculate the products. (1) * (2) = 2 and (2) * (1) = 2.
Step 6: Add the results of the products together. 2 + 2 = 4.
Step 7: Conclude that the dot product A · B = 4.

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