JEE Advanced Model Paper 2 with solutions for online practice

|

→

a

| = |

→

b

| = |

→

c

| = 1 ⇒

→

a

.

→

b

=

→

b

.

→

c

=

→

c

.

→

a

= 1/2
Also

→

a

×

→

b

+

→

b

×

→

c

= p

→

a

+ q

→

b

+ r

→

c

⇒

→

a

.(

→

b

×

→

c

) = p + q (

→

a

.

→

b

) + r (

→

a

.

→

c

)
∴ p +

q

2

+

r

2

= [

→

a

→

b

→

c

] ..... (i)
Similarly, taking dot product with vector

→

b

we get

p

2

+ q

r

2

..... (ii)
And, taking dot product with vector

→

c

, we get

p

2

+

q

2

+ r = [

→

a

→

b

→

c

] .... (iii)
Solving, (i) , (ii) and (iii), we get p = r = -q ⇒

p2+2q2+3r2

q2

= 6