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If A = (a, b, c) and B = (1, 2, 3) such that A · B = 0, what is the relation bet

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Question: If A = (a, b, c) and B = (1, 2, 3) such that A · B = 0, what is the relation between a, b, and c?

Options:

  1. a + 2b + 3c = 0
  2. a - 2b + 3c = 0
  3. a + b + c = 0
  4. a - b - c = 0

Correct Answer: a + 2b + 3c = 0

Solution: 

A · B = a*1 + b*2 + c*3 = 0. Thus, a + 2b + 3c = 0.

If A = (a, b, c) and B = (1, 2, 3) such that A · B = 0, what is the relation bet

Practice Questions

Q1
If A = (a, b, c) and B = (1, 2, 3) such that A · B = 0, what is the relation between a, b, and c?
  1. a + 2b + 3c = 0
  2. a - 2b + 3c = 0
  3. a + b + c = 0
  4. a - b - c = 0

Questions & Step-by-Step Solutions

If A = (a, b, c) and B = (1, 2, 3) such that A · B = 0, what is the relation between a, b, and c?
  • 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: Simplify the expression: A · B = a + 2b + 3c.
  • Step 5: Set the dot product equal to 0, since A · B = 0: a + 2b + 3c = 0.
  • Step 6: This equation (a + 2b + 3c = 0) shows the relationship between a, b, and c.
  • Dot Product – The dot product of two vectors is calculated by multiplying corresponding components and summing the results.
  • Linear Equation – The equation derived from the dot product represents a linear relationship between the variables a, b, and c.
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