EAMCET Engineering 2010 Solved Paper

Given that,

→

a

=

^

i

−2

^

j

+3

^

k

→

b

=2

^

i

+3

^

j

−

^

k

and

→

c

=λ

^

i

+

^

j

+(2λ−1)

^

k

Also, since

→

a

and

→

b

lies in the same plane, then (

→

a

×

→

b

) is perpendicular vector to this plane.
Given that vector

→

c

is parallel to the plane containing

→

a

and

→

b

, so vector (

→

a

×

→

b

) also perpendicular to the vector

→

c

ie,(θ=90∘)
So, (

→

a

×

→

b

)⋅

→

c

should be equal to zero
or ‌(

→

a

×

→

b

)⋅

→

c

=0 . . . (i)

→

a

×

→

b

‌=|

^ i	^ j	^ k
1	−2	3
2	3	−1

|
=‌(2−9)

^

i

+(6+1)

^

j

+(3+4)

^

k

=‌−7

^

i

+7

^

j

+7

^

k

Then from Eq. (i)
‌(−7

^

i

+7

^

j

+7

^

k

)⋅(λ

^

i

+

^

j

+(2λ−1)

^

k

)=0
‌⇒‌‌−7λ+7+7(2λ−1)=0
⇒−7λ+7+14λ−7=0
⇒7λ=0
⇒λ=0
Hence, the value of λ is 0 .