What is the projection of vector A = 3i + 4j onto vector B = 2i + 2j?
Practice Questions
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What is the projection of vector A = 3i + 4j onto vector B = 2i + 2j?
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Projection = (A · B / |B|^2) * B = (14 / 8) * (2i + 2j) = (7/4)(2i + 2j) = 3.5i + 3.5j.
Questions & Step-by-step Solutions
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Q
Q: What is the projection of vector A = 3i + 4j onto vector B = 2i + 2j?
Solution: Projection = (A · B / |B|^2) * B = (14 / 8) * (2i + 2j) = (7/4)(2i + 2j) = 3.5i + 3.5j.
Steps: 7
Step 1: Identify the vectors A and B. A = 3i + 4j and B = 2i + 2j.
Step 2: Calculate the dot product of A and B, denoted as A · B. This is done by multiplying the corresponding components: (3 * 2) + (4 * 2) = 6 + 8 = 14.
Step 3: Calculate the magnitude squared of vector B, denoted as |B|^2. This is done by squaring the components of B: (2^2) + (2^2) = 4 + 4 = 8.
Step 4: Use the formula for projection of A onto B: Projection = (A · B / |B|^2) * B. Substitute the values: (14 / 8) * B.
