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If A = (x, y, z) and B = (1, 1, 1) such that A · B = 6, find x + y + z.

Practice Questions

Q1
If A = (x, y, z) and B = (1, 1, 1) such that A · B = 6, find x + y + z.
  1. 3
  2. 6
  3. 9
  4. 12

Questions & Step-by-Step Solutions

If A = (x, y, z) and B = (1, 1, 1) such that A · B = 6, find x + y + z.
  • Step 1: Understand that A = (x, y, z) and B = (1, 1, 1).
  • Step 2: Know that the dot product A · B is calculated as x * 1 + y * 1 + z * 1.
  • Step 3: Simplify the dot product: A · B = x + y + z.
  • Step 4: We are given that A · B = 6.
  • Step 5: Set up the equation: x + y + z = 6.
  • Step 6: The question asks for the value of x + y + z, which we found to be 6.
  • Dot Product – The dot product of two vectors A and B is calculated as A · B = x1*x2 + y1*y2 + z1*z2.
  • Vector Components – Understanding that A = (x, y, z) and B = (1, 1, 1) means each component of A is multiplied by the corresponding component of B.
  • Algebraic Manipulation – Solving for the sum of the components x, y, and z based on the result of the dot product.
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