NIMCET 2011 Question Paper with solutions

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Question : 38 of 120

Marks: +1, -0

If

{a}, {b}

and

{c}

are unit coplanar vectors, then the scalar triple product

[2 a-b, 2 b-c, 2 c-a]

will be equal to

0
1
$-√3$
$√3$

Solution:

∴ (2 a-b) ⋅[(2 b-c) ×(2 c-a)]

=(2 a-b) ⋅[(2 b × 2 c)-(2 b × a)-0+(c × a)]

=\{8[ a\;b \;c]- {0}+ {0}- {0}+0-[ {b} {c} {a}]\}

=7[a\; b\;c]=0 \;\; [ ∵ {a} {b} {c}=0

(given)]

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