NIMCET 2009 Question Paper with solutions

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Question : 12 of 120

Marks: +1, -0

The vector

B=3 i+4 k

is to be written as the sum of a vector

B_{1}

parallel to

A=i+j

and a vector

µB_{2}

perpendicular to A , then

B_{1}

is

$\;{3}/{2}(i+j)$
$\;{2}/{3}(i+j)$
$\;{1}/{2}(i+j)$
None of these

Solution:

Given,

B_{1}=λ A=λ( {i}+ {j})

B_{2} ⋅ A=0

⇒ \;\; (B-B_{1}) ⋅ A=0 \;\; [ ∵ B=B_{1}+B_{2}

(given)

⇒ \;\; B ⋅ A=B_{1} ⋅ A

(3 i+4 k) ⋅(i+j)=λ(A ⋅ A)=λ(1+1)

⇒ \;\; 3=λ+λ=2 λ

⇒ \;\; λ=\;{3}/{2}

⇒ \;\; ∴ \;\; B_{1}=\;{3}/{2}(i+j)

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