NIMCET 2009 Question Paper with solutions

© examsiri.com

Question : 27 of 120

Marks: +1, -0

a, b, c

are non-coplanar unit vectors such that

a ×(b × c)=\;{b+c}/{√{2}}

, then the angle between

a

and

b

is

$\;{π}/{4}$
$\;{3 π}/{4}$
$\;{π}/{2}$
$π$

Solution:

a ⋅ x(b × c)=(a ⋅ c) b-(a ⋅ b) c

...(i)

a ×(c × c)=\;{b+c}/{√{2}}

.....(ii)
From Eqs. (i) and (ii)

{a} ⋅ {c}=\;{1}/{√{2}}

and

{a} ⋅ {b}=-\;{1}/{√{2}}

a ⋅ b=-\;{1}/{√{2}}

Let

θ

be the angle between

a+b

.

⇒ \;\;{ |a|.|b| }\cos θ=-\;{1}/{√{2}}

⇒ \;\; \cos θ=-\;{1}/{√{2}}

⇒ \;\; θ=\;{3 π}/{4}

© examsiri.com

Go to Question:

Prev Question

Next Question