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If vector A = 2i + 3j and vector B = 4i + 6j, are the vectors A and B parallel?

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Question: If vector A = 2i + 3j and vector B = 4i + 6j, are the vectors A and B parallel?

Options:

  1. Yes
  2. No
  3. Cannot be determined
  4. Only if scaled

Correct Answer: Yes

Solution: 

Vectors A and B are parallel because B = 2A.

If vector A = 2i + 3j and vector B = 4i + 6j, are the vectors A and B parallel?

Practice Questions

Q1
If vector A = 2i + 3j and vector B = 4i + 6j, are the vectors A and B parallel?
  1. Yes
  2. No
  3. Cannot be determined
  4. Only if scaled

Questions & Step-by-Step Solutions

If vector A = 2i + 3j and vector B = 4i + 6j, are the vectors A and B parallel?
  • 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 6j.
  • Step 3: Check if vector B can be expressed as a multiple of vector A.
  • Step 4: Calculate 2 times vector A: 2A = 2(2i + 3j) = 4i + 6j.
  • Step 5: Compare the result of 2A with vector B. Since 2A = B, they are equal.
  • Step 6: Conclude that since B is a multiple of A, vectors A and B are parallel.
  • Vector Parallelism – Two vectors are parallel if one is a scalar multiple of the other.
  • Vector Representation – Understanding how to represent vectors in component form (i, j) and how to manipulate them.
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