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

Practice Questions

Q1
What is the unit vector in the direction of v = (3, 4)?
  1. (0.6, 0.8)
  2. (1, 1)
  3. (3, 4)
  4. (0, 0)

Questions & Step-by-Step Solutions

What is the unit vector in the direction of v = (3, 4)?
  • Step 1: Identify the vector v, which is given as (3, 4).
  • Step 2: Calculate the magnitude (length) of the vector v using the formula |v| = √(x^2 + y^2), where x = 3 and y = 4.
  • Step 3: Substitute the values into the formula: |v| = √(3^2 + 4^2) = √(9 + 16) = √25 = 5.
  • Step 4: To find the unit vector, divide each component of the vector v by its magnitude: unit vector = v / |v|.
  • Step 5: Perform the division: unit vector = (3/5, 4/5).
  • Step 6: Simplify the fractions: unit vector = (0.6, 0.8).
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