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Vectors and 3D Geometry

Vector Algebra, Projection

jee_main_2026_jan_22_shift_1

Grade None

Question:

Let \(\vec{a} = 2\hat{i} + 3\hat{j} + 6\hat{k}\) and \(\vec{b} = \hat{i} + 2\hat{j} + 2\hat{k}\). Find the projection of \(\vec{a}\) on \(\vec{b}\).

A. 2

B. 4

C. 6

D. 20/3

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| = √(1² + 2² + 2²) = 3. Step 3: Projection = 20/3.

Correct Answer: D

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