If A = 2i + 3j and B = 3i + 4j, what is the scalar product A · B?

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Question: If A = 2i + 3j and B = 3i + 4j, what is the scalar product A · B?

Options:

Correct Answer: 18

Solution:

A · B = (2)(3) + (3)(4) = 6 + 12 = 18.

If A = 2i + 3j and B = 3i + 4j, what is the scalar product A · B?

If A = 2i + 3j and B = 3i + 4j, what is the scalar product A · B?

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 = 3i + 4j means B has a component of 3 in the i direction and 4 in the j direction.
Step 3: Calculate the product of the i components of A and B. Multiply 2 (from A) by 3 (from B): (2)(3) = 6.
Step 4: Calculate the product of the j components of A and B. Multiply 3 (from A) by 4 (from B): (3)(4) = 12.
Step 5: Add the results from Step 3 and Step 4 together. 6 + 12 = 18.
Step 6: The scalar product A · B is 18.

Vector Operations – Understanding how to perform operations on vectors, specifically the scalar (dot) product.
Component-wise Multiplication – Recognizing that the scalar product involves multiplying corresponding components of the vectors.