IIT JEE Advanced 2006 Paper 1

Let us consider a coplanar vector

→

r

=

→

a

+λ

→

b

which is coplanar to

→

a

and

→

b

. We get

→

r

= (

^

i

+

^

j

+

^

k

)+λ(

^

i

−

^

j

+

^

k

)

→

r

=

^

i

(1+λ)+

^

j

(2−λ)+

^

k

(1+λ)
Projection of

→

r

on

→

c

is

→

r

.

^

c

=

1

√3

⇒ [i (1 + λ) + j (2 - λ) + k (1 + λ)] (

i−j−k

√3

) =

1

√3

⇒ 1+ λ - 2 + λ - 1- λ
⇒λ – 2 = 1
⇒λ = 3
Therefore,