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

Practice Questions

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

Questions & Step-by-Step Solutions

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