For vectors A = (2, 3) and B = (4, 5), find the scalar product A · B.

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Question: For vectors A = (2, 3) and B = (4, 5), find the scalar product A · B.

Options:

Correct Answer: 23

Solution:

A · B = 2*4 + 3*5 = 8 + 15 = 23.

For vectors A = (2, 3) and B = (4, 5), find the scalar product A · B.

For vectors A = (2, 3) and B = (4, 5), find the scalar product A · B.

Step 1: Identify the components of vector A, which are 2 and 3.
Step 2: Identify the components of vector B, which are 4 and 5.
Step 3: Multiply the first component of A (which is 2) by the first component of B (which is 4). This gives you 2 * 4 = 8.
Step 4: Multiply the second component of A (which is 3) by the second component of B (which is 5). This gives you 3 * 5 = 15.
Step 5: Add the results from Step 3 and Step 4 together. So, 8 + 15 = 23.
Step 6: The scalar product A · B is 23.

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