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

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Question: What is the projection of vector A = (3, 4) onto vector B = (1, 2)?

Options:

Correct Answer: 3

Solution:

Projection = (A . B / |B|^2) * B = (3*1 + 4*2) / (1^2 + 2^2) * (1, 2) = 11/5 * (1, 2) = (2.2, 4.4).

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

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

Step 1: Identify the vectors A and B. Here, A = (3, 4) and B = (1, 2).
Step 2: Calculate the dot product of A and B. This is done by multiplying the corresponding components and adding them: A . B = 3*1 + 4*2.
Step 3: Compute the dot product: A . B = 3 + 8 = 11.
Step 4: Calculate the magnitude squared of vector B. This is done by squaring each component of B and adding them: |B|^2 = 1^2 + 2^2.
Step 5: Compute the magnitude squared: |B|^2 = 1 + 4 = 5.
Step 6: Use the formula for projection: Projection = (A . B / |B|^2) * B.
Step 7: Substitute the values into the formula: Projection = (11 / 5) * (1, 2).
Step 8: Multiply the scalar (11/5) by each component of vector B: (11/5) * (1, 2) = (11/5 * 1, 11/5 * 2).
Step 9: Calculate the components: (11/5, 22/5) = (2.2, 4.4).
Step 10: The final result is the projection of vector A onto vector B, which is (2.2, 4.4).

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