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If G = (1, 1, 1) and H = (1, -1, 1), what is G · H?

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Question: If G = (1, 1, 1) and H = (1, -1, 1), what is G · H?

Options:

  1. 0
  2. 1
  3. 2
  4. -1

Correct Answer: 0

Solution: 

G · H = 1*1 + 1*(-1) + 1*1 = 1 - 1 + 1 = 1.

If G = (1, 1, 1) and H = (1, -1, 1), what is G · H?

Practice Questions

Q1
If G = (1, 1, 1) and H = (1, -1, 1), what is G · H?
  1. 0
  2. 1
  3. 2
  4. -1

Questions & Step-by-Step Solutions

If G = (1, 1, 1) and H = (1, -1, 1), what is G · H?
Correct Answer: 1
  • Step 1: Identify the components of vectors G and H. G has components (1, 1, 1) and H has components (1, -1, 1).
  • Step 2: Multiply the corresponding components of G and H. This means you will calculate 1*1, 1*(-1), and 1*1.
  • Step 3: Calculate each multiplication: 1*1 = 1, 1*(-1) = -1, and 1*1 = 1.
  • Step 4: Add the results of the multiplications together: 1 + (-1) + 1.
  • Step 5: Simplify the addition: 1 - 1 + 1 = 1.
  • Dot Product – The dot product of two vectors is calculated by multiplying their corresponding components and summing the results.
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