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

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

Options:

Correct Answer: 5

Solution:

proj_B(A) = (A · B / |B|^2)B = ((3*1 + 4*1) / (1^2 + 1^2))(i + j) = (7/2)(i + j) = 3.5.

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

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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