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What is the magnitude of the vector v = (3, -4)?

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Question: What is the magnitude of the vector v = (3, -4)?

Options:

  1. 5
  2. 7
  3. 4
  4. 3

Correct Answer: 5

Solution: 

Magnitude of v = √(3^2 + (-4)^2) = √(9 + 16) = √25 = 5.

What is the magnitude of the vector v = (3, -4)?

Practice Questions

Q1
What is the magnitude of the vector v = (3, -4)?
  1. 5
  2. 7
  3. 4
  4. 3

Questions & Step-by-Step Solutions

What is the magnitude of the vector v = (3, -4)?
  • Step 1: Identify the components of the vector v. Here, v = (3, -4), so the components are 3 and -4.
  • Step 2: Use the formula for the magnitude of a vector, which is √(x^2 + y^2), where x and y are the components of the vector.
  • Step 3: Substitute the values of the components into the formula. This gives us √(3^2 + (-4)^2).
  • Step 4: Calculate 3^2, which is 9.
  • Step 5: Calculate (-4)^2, which is 16.
  • Step 6: Add the results from Step 4 and Step 5. So, 9 + 16 = 25.
  • Step 7: Take the square root of 25. This gives us √25 = 5.
  • Step 8: Conclude that the magnitude of the vector v is 5.
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