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

Practice Questions

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

Questions & Step-by-Step Solutions

What is the unit vector in the direction of the vector (4, 3)?
  • Step 1: Identify the given vector, which is (4, 3).
  • Step 2: Calculate the magnitude of the vector using the formula: magnitude = sqrt(x^2 + y^2), where x = 4 and y = 3.
  • Step 3: Substitute the values into the formula: magnitude = sqrt(4^2 + 3^2) = sqrt(16 + 9) = sqrt(25) = 5.
  • Step 4: To find the unit vector, divide each component of the vector by its magnitude. The unit vector = (4/magnitude, 3/magnitude).
  • Step 5: Substitute the magnitude into the equation: unit vector = (4/5, 3/5).
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