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Vectors and 3D Geometry

Vectors, Projection

jee_main_2026_april_4_shift_2

Grade 12

Question:

If a = 2i + 3j + 6k, and b = i + 2j + 2k, find the projection of a on b.

A. 2

B. 3

C. 20/3

D. 4

Step-by-Step Solution

Key Concept: Projection of a on b = (a·b)/|b|.

Step 1: a·b = (2)(1) + (3)(2) + (6)(2) = 2 + 6 + 12 = 20. Step 2: |b| = √(1^2 + 2^2 + 2^2) = √9 = 3. Step 3: Projection = 20/3.

Correct Answer: C

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