Write the value of p for which a^{\to} = ...

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↖{→}

=

3i↖{\^}+2j↖{\^}+9k↖{\^}

and

b↖{→}

=

i↖{\^}+pj↖{\^}+3k↖{\^}

are parallel vectors.

Solution:

Two vectors

a↖{→}

and

b↖{→}

are parallel

a↖{→}

=

3i↖{\^}+2j↖{\^}+9k↖{\^}

and

b↖{→}

=

i↖{\^}+pj↖{\^}+3k↖{\^}

a↖{→}

= λ

b↖{→}

So

3i↖{\^}+2j↖{\^}+9k↖{\^}

= λ

(i↖{\^}+pj↖{\^}+3k↖{\^})

⇒

3i↖{\^}+2j↖{\^}+9k↖{\^}

=

λi↖{\^}+λpj↖{\^}+λ3k↖{\^}

⇒ λ = 3 , pλ = 2 and 9 = 3λ
⇒ p =

2/3

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