Calculate the scalar product of the vectors (1, 2, 3) and (4, 5, 6).

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Question: Calculate the scalar product of the vectors (1, 2, 3) and (4, 5, 6).

Options:

Correct Answer: 32

Solution:

Scalar product = 1*4 + 2*5 + 3*6 = 4 + 10 + 18 = 32.

Calculate the scalar product of the vectors (1, 2, 3) and (4, 5, 6).

Calculate the scalar product of the vectors (1, 2, 3) and (4, 5, 6).

Step 1: Identify the first vector, which is (1, 2, 3).
Step 2: Identify the second vector, which is (4, 5, 6).
Step 3: Multiply the first component of the first vector (1) by the first component of the second vector (4). This gives you 1 * 4 = 4.
Step 4: Multiply the second component of the first vector (2) by the second component of the second vector (5). This gives you 2 * 5 = 10.
Step 5: Multiply the third component of the first vector (3) by the third component of the second vector (6). This gives you 3 * 6 = 18.
Step 6: Add all the results from Steps 3, 4, and 5 together: 4 + 10 + 18.
Step 7: Calculate the total: 4 + 10 = 14, then 14 + 18 = 32.

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