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If the vector a = (2, 3, 4) is scaled by a factor of 2, what is the resulting ve

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Question: If the vector a = (2, 3, 4) is scaled by a factor of 2, what is the resulting vector?

Options:

  1. (4, 6, 8)
  2. (2, 3, 4)
  3. (1, 1.5, 2)
  4. (0, 0, 0)

Correct Answer: (4, 6, 8)

Solution: 

Scaling the vector a by 2 gives (2*2, 2*3, 2*4) = (4, 6, 8).

If the vector a = (2, 3, 4) is scaled by a factor of 2, what is the resulting ve

Practice Questions

Q1
If the vector a = (2, 3, 4) is scaled by a factor of 2, what is the resulting vector?
  1. (4, 6, 8)
  2. (2, 3, 4)
  3. (1, 1.5, 2)
  4. (0, 0, 0)

Questions & Step-by-Step Solutions

If the vector a = (2, 3, 4) is scaled by a factor of 2, what is the resulting vector?
  • Step 1: Identify the original vector a, which is (2, 3, 4).
  • Step 2: Determine the scaling factor, which is 2.
  • Step 3: Multiply each component of the vector a by the scaling factor. This means:
  • Step 4: Calculate the first component: 2 * 2 = 4.
  • Step 5: Calculate the second component: 3 * 2 = 6.
  • Step 6: Calculate the third component: 4 * 2 = 8.
  • Step 7: Combine the results from steps 4, 5, and 6 to form the new vector: (4, 6, 8).
  • Vector Scaling – Scaling a vector involves multiplying each component of the vector by a scalar value.
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