VITEEE 2015 Paper

Vector perpendicular to face OAB =

→

n1

=

→

OA

×

→

OB

= (

^

i

−2

^

j

+

^

k

) × (−2

^

i

+

^

j

+

^

k

)
= (- 2 - 1)

^

i

+ (- 2 - 1)

^

j

+ (1 - 4)

^

k

= −3

^

i

−3

^

j

−3

^

k

Vector perpendicular to face ABC =

→

n2

=

→

AB

×

→

AC

= (3

^

i

+3

^

j

)×(

^

j

+

^

k

)
= −3

^

i

+3

^

j

−3

^

k

Since, angle between faces is equal to angle between their normals.
∴ cos θ =

→ n1 . → n2

|n1||n2|

=
=

−9−9+9

√27√27

= -

1

3

⇒ θ = cos−1(−

1

3

)