Find the scalar product of A = (1, 2, 3) and B = (4, 5, 6).

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Question: Find the scalar product of A = (1, 2, 3) and B = (4, 5, 6).

Options:

Correct Answer: 30

Solution:

A · B = 1*4 + 2*5 + 3*6 = 4 + 10 + 18 = 32.

Find the scalar product of A = (1, 2, 3) and B = (4, 5, 6).

Find the scalar product of A = (1, 2, 3) and B = (4, 5, 6).

Step 1: Identify the components of vector A, which are (1, 2, 3).
Step 2: Identify the components of vector B, which are (4, 5, 6).
Step 3: Multiply the first component of A (1) by the first component of B (4). This gives 1 * 4 = 4.
Step 4: Multiply the second component of A (2) by the second component of B (5). This gives 2 * 5 = 10.
Step 5: Multiply the third component of A (3) by the third component of B (6). This gives 3 * 6 = 18.
Step 6: Add the results from Steps 3, 4, and 5 together: 4 + 10 + 18.
Step 7: Calculate the sum: 4 + 10 = 14, then 14 + 18 = 32.
Step 8: The scalar product of A and B is 32.

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