If A = 6i + 8j and B = 2i + 3j, what is the scalar product A · B?

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Question: If A = 6i + 8j and B = 2i + 3j, what is the scalar product A · B?

Options:

Correct Answer: 36

Solution:

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

If A = 6i + 8j and B = 2i + 3j, what is the scalar product A · B?

If A = 6i + 8j and B = 2i + 3j, what is the scalar product A · B?

Step 1: Identify the components of vector A. A = 6i + 8j means A has a component of 6 in the i direction and 8 in the j direction.
Step 2: Identify the components of vector B. B = 2i + 3j means B has a component of 2 in the i direction and 3 in the j direction.
Step 3: Calculate the product of the i components of A and B. Multiply 6 (from A) by 2 (from B): 6 * 2 = 12.
Step 4: Calculate the product of the j components of A and B. Multiply 8 (from A) by 3 (from B): 8 * 3 = 24.
Step 5: Add the results from Step 3 and Step 4 together. 12 + 24 = 36.
Step 6: The scalar product A · B is 36.

Vector Operations – Understanding how to compute the scalar (dot) product of two vectors.
Component Multiplication – Applying the formula for the dot product by multiplying corresponding components of the vectors.