Find 'λ' when the projection of a^{\to} = \lambdai^{\^}+j^{\^}+4k^{\^} on b^{\to} = 2i^{\^}+6j^{\^}+3k^{\^} is 4 units

CBSE Class 12 Math 2012 Solved Paper - Question 4

Question : 4 of 29

Marks: +1, -0

Find 'λ' when the projection of

a↖{→}

λi↖{\^}+j↖{\^}+4k↖{\^}

b↖{→}

2i↖{\^}+6j↖{\^}+3k↖{\^}

is 4 units

Solution:

Projection of

a↖{→}

b↖{→}

{a↖{→}.b↖{→}}/{|b↖{→}|}

= 4 (given)
⇒

{(λi↖{\^}+j↖{\^}+4k↖{\^}).(2i↖{\^}+6j↖{\^}+3k↖{\^})}/√{2^2+6^2+3^2}

= 4
⇒

{2λ + 6 +12}/7

= 4
⇒ λ = 5

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