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CBSE Class 12 Math 2012 Solved Paper

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Question : 4 of 29
Marks: +1, -0
Find 'λ' when the projection of a⃗\vec{a} = λi^+j^+4k^\lambda\hat{i}+\hat{j}+\hat{4k} on b⃗\vec{b} = 2i^+6j^+3k^\hat{2i}+\hat{6j}+\hat{3k} is 4 units
Solution:  
Projection of a⃗\vec{a} on b⃗\vec{b} = a⃗⋅b⃗∣b⃗∣\frac{\vec{a}\cdot\vec{b}}{\left|\vec{b}\right|} = 4 (given)
⇒
(λi^+j^+4k^)⋅(2i^+6j^+3k^)22+62+32\frac{(\lambda\hat{i}+\hat{j}+\hat{4k})\cdot(\hat{2i}+\hat{6j}+\hat{3k})}{\sqrt{2^2+6^2+3^2}}
= 4
⇒ 2λ+6+127\frac{2\lambda+6+12}{7} = 4
⇒ λ = 5
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