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

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

Options:

Correct Answer: 14

Solution:

A · B = (2)(3) + (1)(4) = 6 + 4 = 10.

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

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

Step 1: Identify the components of vector A. A = 2i + j means A has a component of 2 in the i direction and 1 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 (2)(3) = 6.
Step 4: Multiply the j components of A and B together. This is (1)(4) = 4.
Step 5: Add the results from Step 3 and Step 4 together. This is 6 + 4 = 10.
Step 6: The scalar product A · B is 10.

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