IIT JEE Advanced 2006 Paper 1

The direction ratio of plane P1 is |

∧ i	∧ j	∧ k
0	2	3
0	4	−3
‌	‌	‌

|=i(−6−12)=−18i
That is, (−18,0,0)⇒(1,0,0). The direction ratio of plane P2 is
|

∧ i	∧ j	∧ k
0	1	−1
3	0	3
‌	‌	‌

|=

∧

i

(3)−

∧

j

(3)+

∧

k

(−3)
That is, (3,−3,−3)⇒(1,−1,−1).
The direction ratio of line of intersection is
|

∧ i	∧ j	∧ k
1	0	0
1	−1	−1
‌	‌	‌

|=−(−

∧

j

+

∧

k

)=

∧

j

−

∧

k

The angle between

→

A

and 2

∧

i

+

∧

j

−2

∧

k

is
cos‌θ=‌

1+2

√2×3

=‌

1

√2

⇒θ=‌

π

4

=‌

3π

4