Three Dimensional Geometry
Consider the lines and the planes Let ax + by + cz = d be the equation of the plane passing through the point of intersection of lines L_{1} and L_{2}, and perpendicular to planes P_{ 1} and P_{2}.
Match List − I with List − II and select the correct answer using the code given below the lists:

List I 

List II 
P. 
a = 
1. 
13 
Q. 
b = 
2. 
–3 
R. 
c = 
3. 
1 
S. 
d = 
4. 
–2 
Match the statements in column I with those in column II.
Column I 
Column II 

(A) 
A line from the origin meets the lines and at P and Q respectively. If length PQ = d, then d^{2} is 
(p) 
4 
(B) 
The values of x satisfying are 
(q) 
0 
(C) 
Nonzero vectors satisfy , and Then the possible values of are

(r) 
4 
(D) 
Let f be the function on given by f(0) = 9 and f(x) = (s) for . The value of is 
(s) 
5 
(t) 
6 
Match the statements / expression in Column I with the open intervals in Column II
Column I 
Column II 

(A) 
The number of solutions of the equation in the interval 
(p) 
1 
(B) 
Value(s) of for which the planes and intersect in a straight line 
(q) 
2 
(C) 
Value(s) of for which _{ }has integer solution(s) 
(r) 
3 
(D) 
If and then the value(s) of 
(s) 
4 
(t) 
5 
Match the following:
(i)  If $\sum _{i=1}^{\infty}{\mathrm{tan}}^{1}\left(\frac{1}{2{i}^{2}}\right)=t$, then tan t =  (A) 2/3 
(ii)  Sides a, b, c of a triangle ABC are in AP and $\mathrm{cos}{\theta}_{1}=\frac{a}{b+c},\mathrm{cos}{\theta}_{2}=\frac{b}{a+c},\mathrm{cos}{\theta}_{3}=\frac{c}{a+b},$ then tan^{2} $\left(\frac{{\theta}_{1}}{2}\right)+{\mathrm{tan}}^{2}\left(\frac{{\theta}_{3}}{2}\right)=$  (B) 1 
(iii)  A line is perpendicular to x + 2y + 2z = 0 and passes through point (0, 1, 0). The perpendicular distance of this line from the origin is  (C) $\frac{\sqrt{5}}{3}$ 