If A = 6i + 8j and B = 3i + 4j, what is the scalar product A · B?

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Question: If A = 6i + 8j and B = 3i + 4j, what is the scalar product A · B?

Options:

Correct Answer: 54

Solution:

A · B = (6)(3) + (8)(4) = 18 + 32 = 50.

If A = 6i + 8j and B = 3i + 4j, what is the scalar product A · B?

If A = 6i + 8j and B = 3i + 4j, 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 = 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 together. This is 6 (from A) times 3 (from B), which equals 18.
Step 4: Multiply the j components of A and B together. This is 8 (from A) times 4 (from B), which equals 32.
Step 5: Add the results from Step 3 and Step 4 together. This is 18 + 32, which equals 50.
Step 6: The final result, A · B, is 50.

Vector Operations – Understanding how to perform operations on vectors, specifically the scalar (dot) product.
Component-wise Multiplication – Applying the formula for the scalar product by multiplying corresponding components of the vectors.