What is the projection of vector A = 3i + 4j onto vector B = 1i + 2j?

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Question: What is the projection of vector A = 3i + 4j onto vector B = 1i + 2j?

Options:

Correct Answer: 2.5

Solution:

Projection = (A · B / |B|^2) * B = (11 / 5) * (1i + 2j) = 2.5.

What is the projection of vector A = 3i + 4j onto vector B = 1i + 2j?

What is the projection of vector A = 3i + 4j onto vector B = 1i + 2j?

Step 1: Identify the vectors A and B. A = 3i + 4j and B = 1i + 2j.
Step 2: Calculate the dot product of A and B, which is A · B = (3 * 1) + (4 * 2) = 3 + 8 = 11.
Step 3: Calculate the magnitude squared of vector B, which is |B|^2 = (1^2) + (2^2) = 1 + 4 = 5.
Step 4: Divide the dot product by the magnitude squared of B: A · B / |B|^2 = 11 / 5.
Step 5: Multiply the result by vector B to find the projection: (11 / 5) * (1i + 2j).
Step 6: Distribute (11 / 5) to both components of B: (11/5) * 1i + (11/5) * 2j = (11/5)i + (22/5)j.
Step 7: The final projection vector is (11/5)i + (22/5)j.

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