NIMCET 2020 Question Paper with solutions

Question : 35 of 120

Marks: +1, -0

If a, b, c are three non-zero vectors with no two of which are collinear,

a +2 b

is collinear with c and

b +3 c

is collinear with a , then

a +2 b + 6c

will be equal to

Solution:

Given

a↖{→}+2b↖{→}=λc↖{→}

a+2b+3c↖{→}=(λ+3)c↖{→}

......(1)

b+3c↖{→}=µa↖{→}

a+2(b+3c↖{→})=(1+2µ)a↖{→}

......(2)
From (1) and (2)

(λ+3)c↖{→}=(1+2µ)a↖{→}

Because

c↖{→}

and

a↖{→}

are non-collinear.
Then

a↖{→}+2b↖{→}+6c↖{→}=0↖{→}

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