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What is the projection of vector A = 3i + 4j onto vector B = i + j? (2020)

Practice Questions

Q1
What is the projection of vector A = 3i + 4j onto vector B = i + j? (2020)
  1. 3
  2. 4
  3. 5
  4. 7

Questions & Step-by-Step Solutions

What is the projection of vector A = 3i + 4j onto vector B = i + j? (2020)
  • Step 1: Identify the vectors A and B. A = 3i + 4j and B = i + j.
  • Step 2: Calculate the dot product of A and B. A · B = (3 * 1) + (4 * 1) = 3 + 4 = 7.
  • Step 3: Calculate the magnitude squared of vector B. |B|^2 = (1^2) + (1^2) = 1 + 1 = 2.
  • Step 4: Use the formula for the projection of A onto B: proj_B(A) = (A · B / |B|^2)B.
  • Step 5: Substitute the values into the formula: proj_B(A) = (7 / 2)(i + j).
  • Step 6: Simplify the expression: proj_B(A) = (7/2)(i + j) = 3.5(i + j).
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