What is the projection of the vector a = 2 i + 3 j + 2 k on the vector b = i + 2 j + k?
Answer and explanation
Correct answer: B. 5√6 / 3
- Step 1: Projection formula: Proj_b(a) = (a · b) / |b|.
- Step 2: a · b = 2(1) + 3(2) + 2(1) = 2 + 6 + 2 = 10.
- Step 3: |b| = sqrt(1^2 + 2^2 + 1^2) = sqrt(6).
- Step 4: Projection = 10 / √6 = 10√6 / 6 = 5√6 / 3.
Why not the others: The other values (4√6 / 3, 5 / √6, 2√6) arise from summing vector components linearly without squaring, or forgetting to take the square root of the sum.
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