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If A = 2i + 3j and B = 4i + 5j, what is the resultant vector A + B?

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Question: If A = 2i + 3j and B = 4i + 5j, what is the resultant vector A + B?

Options:

  1. 6i + 8j
  2. 2i + 3j
  3. 4i + 5j
  4. 8i + 10j

Correct Answer: 6i + 8j

Solution: 

Resultant A + B = (2i + 3j) + (4i + 5j) = (2 + 4)i + (3 + 5)j = 6i + 8j.

If A = 2i + 3j and B = 4i + 5j, what is the resultant vector A + B?

Practice Questions

Q1
If A = 2i + 3j and B = 4i + 5j, what is the resultant vector A + B?
  1. 6i + 8j
  2. 2i + 3j
  3. 4i + 5j
  4. 8i + 10j

Questions & Step-by-Step Solutions

If A = 2i + 3j and B = 4i + 5j, what is the resultant vector A + B?
  • Step 1: Identify the components of vector A, which are 2i and 3j.
  • Step 2: Identify the components of vector B, which are 4i and 5j.
  • Step 3: Add the i components of A and B together: 2i + 4i = 6i.
  • Step 4: Add the j components of A and B together: 3j + 5j = 8j.
  • Step 5: Combine the results from Step 3 and Step 4 to get the resultant vector: 6i + 8j.
  • Vector Addition – Understanding how to add vectors by combining their respective components.
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