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

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

Options:

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

Correct Answer: (6, 8)

Solution: 

New vector = 2 * (3, 4) = (6, 8).

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

Practice Questions

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

Questions & Step-by-Step Solutions

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