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CBSE Class 12 Math 2009 Solved Paper

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Question : 8 of 29
Marks: +1, -0
Write the value of p for which a→\overset{\rightarrow}{a} = 3i^+2j^+9k^\hat{3i}+\hat{2j}+\hat{9k} and b→\overset{\rightarrow}{b} = i^+pj^+3k^\hat{i}+\hat{pj}+\hat{3k} are parallel vectors.
Solution:  
Two vectors a→\overset{\rightarrow}{a} and b→\overset{\rightarrow}{b} are parallel
a→\overset{\rightarrow}{a} = 3i^+2j^+9k^\hat{3i}+\hat{2j}+\hat{9k} and b→\overset{\rightarrow}{b} = i^+pj^+3k^\hat{i}+\hat{pj}+\hat{3k}
a→\overset{\rightarrow}{a} = λ b→\overset{\rightarrow}{b}
So 3i^+2j^+9k^\hat{3i}+\hat{2j}+\hat{9k} = λ (i^+pj^+3k^)(\hat{i}+\hat{pj}+\hat{3k})
⇒ 3i^+2j^+9k^\hat{3i}+\hat{2j}+\hat{9k} = λi^+λpj^+λ3k^\lambda\hat{i}+\lambda\hat{pj}+\lambda\hat{3k}
⇒ λ = 3 , pλ = 2 and 9 = 3λ
⇒ p = 23\frac{2}{3}
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