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What is the scalar projection of vector A = (3, 4) onto vector B = (1, 0)?

Practice Questions

Q1
What is the scalar projection of vector A = (3, 4) onto vector B = (1, 0)?
  1. 3
  2. 4
  3. 0
  4. 1

Questions & Step-by-Step Solutions

What is the scalar projection of vector A = (3, 4) onto vector B = (1, 0)?
  • Step 1: Identify vector A and vector B. Here, A = (3, 4) and B = (1, 0).
  • Step 2: Calculate the dot product of A and B. This is done by multiplying the corresponding components of A and B: (3 * 1) + (4 * 0) = 3 + 0 = 3.
  • Step 3: Calculate the magnitude (length) of vector B. The magnitude of B = (1, 0) is calculated as the square root of (1^2 + 0^2) = sqrt(1) = 1.
  • Step 4: Divide the dot product from Step 2 by the magnitude from Step 3 to find the scalar projection: Scalar projection = 3 / 1 = 3.
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