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What is the unit vector in the direction of vector A = 4i + 3j?

Practice Questions

Q1
What is the unit vector in the direction of vector A = 4i + 3j?
  1. (4/5)i + (3/5)j
  2. (3/4)i + (4/3)j
  3. (4/3)i + (3/4)j
  4. (3/5)i + (4/5)j

Questions & Step-by-Step Solutions

What is the unit vector in the direction of vector A = 4i + 3j?
  • Step 1: Identify the vector A. In this case, A = 4i + 3j.
  • Step 2: Calculate the magnitude (length) of vector A. Use the formula |A| = √(4^2 + 3^2).
  • Step 3: Calculate 4^2, which is 16, and 3^2, which is 9.
  • Step 4: Add the results from Step 3: 16 + 9 = 25.
  • Step 5: Take the square root of 25 to find |A|. √25 = 5.
  • Step 6: Now, find the unit vector by dividing vector A by its magnitude: Unit vector = A / |A|.
  • Step 7: Substitute A and |A| into the formula: Unit vector = (4i + 3j) / 5.
  • Step 8: Simplify the expression: Unit vector = (4/5)i + (3/5)j.
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