If A = (a, b, c) and B = (1, 2, 3), what is the scalar product A · B?

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Question: If A = (a, b, c) and B = (1, 2, 3), what is the scalar product A · B?

Options:

Correct Answer: a + 2b + 3c

Solution:

A · B = a*1 + b*2 + c*3 = a + 2b + 3c.

If A = (a, b, c) and B = (1, 2, 3), what is the scalar product A · B?

If A = (a, b, c) and B = (1, 2, 3), what is the scalar product A · B?

Step 1: Identify the components of vector A, which are a, b, and c.
Step 2: Identify the components of vector B, which are 1, 2, and 3.
Step 3: Multiply the first component of A (a) by the first component of B (1). This gives you a * 1.
Step 4: Multiply the second component of A (b) by the second component of B (2). This gives you b * 2.
Step 5: Multiply the third component of A (c) by the third component of B (3). This gives you c * 3.
Step 6: Add all the results from Steps 3, 4, and 5 together: (a * 1) + (b * 2) + (c * 3).
Step 7: Simplify the expression from Step 6 to get the final result: a + 2b + 3c.

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