NIMCET 2011 Question Paper with solutions

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Question : 40 of 120

Marks: +1, -0

Let

v=2 i+j-k

and

w=i+3 k

. If

u

is a unit vector then the maximum value of the scalar triple product

[u v w]

is

$-1$
$-√{10}-√{6}$
$√{59}$
$√{10}+√{6}$

Solution:

Given,

v=2 j+j-k

and

{w}=i+3 k

∴ \;\; | u \;v \;w |= {u} ⋅( {v} × {w}) ≤| {u}|| {v} × {w}| ( ∵ a ⋅ b ≤, {|a||b∣})

⇒ \;\; [ u \;v \;w ] ≤| {v} × {w}| \;\; ( ∵ {|u|}=1)

Now,

\;\; v × w=|\table i , j , k ; 2 , 1 , -1 ; 1 , 0 , 3|=3 i-7 j-k

⇒ {|v ×w|}=√{3^{2}+7^{2}+1^{2}}=√{59}

[u\; v \;w] ≤ √{59}

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