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

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

Options:

Correct Answer: 10

Solution:

A · B = (3)(2) + (4)(-1) = 6 - 4 = 2.

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

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

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

Vector Operations – Understanding how to compute the scalar (dot) product of two vectors using their components.
Component Multiplication – Applying the formula for the scalar product, which involves multiplying corresponding components of the vectors and summing the results.