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If A = (a, b, c) and B = (1, 2, 3), and A · B = 14, what is the equation?

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Question: If A = (a, b, c) and B = (1, 2, 3), and A · B = 14, what is the equation?

Options:

  1. a + 2b + 3c = 14
  2. a - 2b + 3c = 14
  3. a + 2b - 3c = 14
  4. a - 2b - 3c = 14

Correct Answer: a + 2b + 3c = 14

Solution: 

A · B = a*1 + b*2 + c*3 = 14.

If A = (a, b, c) and B = (1, 2, 3), and A · B = 14, what is the equation?

Practice Questions

Q1
If A = (a, b, c) and B = (1, 2, 3), and A · B = 14, what is the equation?
  1. a + 2b + 3c = 14
  2. a - 2b + 3c = 14
  3. a + 2b - 3c = 14
  4. a - 2b - 3c = 14

Questions & Step-by-Step Solutions

If A = (a, b, c) and B = (1, 2, 3), and A · B = 14, what is the equation?
Correct Answer: a + 2b + 3c = 14
  • Step 1: Identify the vectors A and B. A = (a, b, c) and B = (1, 2, 3).
  • Step 2: Understand that A · B means the dot product of A and B.
  • Step 3: Write the formula for the dot product: A · B = a*1 + b*2 + c*3.
  • Step 4: Substitute the values from the vectors into the formula: A · B = a*1 + b*2 + c*3.
  • Step 5: Set the equation equal to 14, as given: a*1 + b*2 + c*3 = 14.
  • Dot Product – The dot product of two vectors is calculated by multiplying corresponding components and summing the results.
  • Vector Notation – Understanding how to represent vectors and their components is crucial for solving problems involving vector operations.
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