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If A = (1, 2, 3) and B = (k, k, k) are perpendicular, what is the value of k?

Practice Questions

Q1
If A = (1, 2, 3) and B = (k, k, k) are perpendicular, what is the value of k?
  1. 1
  2. 2
  3. 3
  4. 0

Questions & Step-by-Step Solutions

If A = (1, 2, 3) and B = (k, k, k) are perpendicular, what is the value of k?
  • Step 1: Understand that two vectors A and B are perpendicular if their dot product is equal to 0.
  • Step 2: Identify the vectors given: A = (1, 2, 3) and B = (k, k, k).
  • Step 3: Write the formula for the dot product of A and B: A · B = 1*k + 2*k + 3*k.
  • Step 4: Simplify the dot product: A · B = k + 2k + 3k = 6k.
  • Step 5: Set the dot product equal to 0 because the vectors are perpendicular: 6k = 0.
  • Step 6: Solve for k by dividing both sides by 6: k = 0.
  • Dot Product – The dot product of two vectors is zero if and only if the vectors are perpendicular.
  • Vector Representation – Understanding how to represent vectors in component form and how to manipulate them algebraically.
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