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If the vector A = 5i + 12j is scaled by a factor of 2, what is the new vector?

Practice Questions

Q1
If the vector A = 5i + 12j is scaled by a factor of 2, what is the new vector?
  1. 10i + 24j
  2. 5i + 12j
  3. 2i + 3j
  4. 7i + 14j

Questions & Step-by-Step Solutions

If the vector A = 5i + 12j is scaled by a factor of 2, what is the new vector?
  • Step 1: Identify the original vector A, which is given as A = 5i + 12j.
  • Step 2: Understand that scaling a vector by a factor means multiplying each component of the vector by that factor.
  • Step 3: Since we are scaling by a factor of 2, we will multiply both components of vector A by 2.
  • Step 4: Multiply the i component: 2 * 5 = 10, so the new i component is 10i.
  • Step 5: Multiply the j component: 2 * 12 = 24, so the new j component is 24j.
  • Step 6: Combine the new components to form the new vector: 10i + 24j.
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