If M = (1, 2, 3) and N = (4, 5, 6), what is the scalar product M · N?

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Question: If M = (1, 2, 3) and N = (4, 5, 6), what is the scalar product M · N?

Options:

Correct Answer: 32

Solution:

M · N = 1*4 + 2*5 + 3*6 = 4 + 10 + 18 = 32.

If M = (1, 2, 3) and N = (4, 5, 6), what is the scalar product M · N?

If M = (1, 2, 3) and N = (4, 5, 6), what is the scalar product M · N?

Step 1: Identify the components of vector M, which are 1, 2, and 3.
Step 2: Identify the components of vector N, which are 4, 5, and 6.
Step 3: Multiply the first component of M (1) by the first component of N (4). This gives 1 * 4 = 4.
Step 4: Multiply the second component of M (2) by the second component of N (5). This gives 2 * 5 = 10.
Step 5: Multiply the third component of M (3) by the third component of N (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 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.