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What is the unit vector in the direction of (3, 4)?

Practice Questions

Q1
What is the unit vector in the direction of (3, 4)?
  1. (3/5, 4/5)
  2. (4/5, 3/5)
  3. (1, 1)
  4. (0, 0)

Questions & Step-by-Step Solutions

What is the unit vector in the direction of (3, 4)?
  • Step 1: Identify the vector you want to find the unit vector for. In this case, the vector is (3, 4).
  • Step 2: Calculate the magnitude (length) of the vector. Use the formula: √(x^2 + y^2), where x and y are the components of the vector.
  • Step 3: Substitute the values into the formula: √(3^2 + 4^2) = √(9 + 16) = √25 = 5.
  • Step 4: Divide each component of the vector by the magnitude to find the unit vector. This means you will calculate (3/5, 4/5).
  • Step 5: The result (3/5, 4/5) is the unit vector in the direction of (3, 4).
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