NIMCET 2012 Question Paper with solutions

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Question : 49 of 120

Marks: +1, -0

If θ (0 ≤ θ ≤ π) is the angle between the vectors a and b, then

{|a×b|}/{a.b}

equals to

$- cot θ$
$t a n θ$
$- tan θ$
$c o t θ$

Solution:

∵ θ ∈[0, π]

Now,

\;{| a × b |}/{ a ⋅ b }=\;{\| a || b |\sin θ( n )|}/{| a || b |(-\cos θ)}

\;\; =\;{| a || b ||\sin θ|| n |}/{| a || b |(-\cos θ)}

\;\; =\;{\sin θ ⋅ 1}/{-\cos θ}=-\tan θ

(\cos θ

in second quadrant is negative)

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