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

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

Options:

Correct Answer: 25

Solution:

A · B = (3)(4) + (4)(3) = 12 + 12 = 24.

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

If the vectors A = 3i + 4j and B = 4i + 3j, 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 = 4i + 3j means B has a component of 4 in the i direction and 3 in the j direction.
Step 3: To find the scalar product A · B, use the formula: A · B = (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 = (3) * (4) + (4) * (3).
Step 5: Calculate the first part: (3) * (4) = 12.
Step 6: Calculate the second part: (4) * (3) = 12.
Step 7: Add the two results together: 12 + 12 = 24.
Step 8: The scalar product A · B is 24.

Vector Scalar Product – The scalar product (or dot product) of two vectors is calculated by multiplying their corresponding components and summing the results.