CBSE Class 12 Sample Paper for 2018 Boards

Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

### Find the Projection (vector) of 2i β j + k on i β 2j + k

This is a question of CBSE Sample Paper - Class 12 - 2017/18.

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### Transcript

Question 11 Find the Projection (vector) of 2π Μ β π Μ + π Μ on π Μ β 2π Μ + π Μ Let a = 2π Μ β π Μ + π Μ and b = π Μ β 2π Μ + π Μ We need to find Projection (vector) of π β on π β Theory We know that Projection of π β on π β = 1/("|" π β"|" ) (π β. π β) But here, we are asked projection (vector) So, we multiply projection by π β/|π β | Projection (vector) of π β on π β = 1/|π β | (π β. π β) Γ π β/|π β | = ((π β . π β ))/|π β |^2 Γ π β (π β. π β) = (2 Γ 1) + (β1 Γ β2) + (1 Γ 1) = 2 + 2 + 1 = 5 Magnitude of π β = β(12+(β2)2+12) |π β | = β(1+4+1) = β6 Projection (vector) of π β on π β = ((π β . π β ))/|π β |^2 Γ π β = 5/(β6)^2 Γ ( π Μ β 2π Μ + π Μ) = π/π ( π Μ β 2π Μ + π Μ)