KEAM 2013 Math Paper

Given equation of line is ‌

x+1

1

=‌

y−1

2

=‌

z−2

2

.
Direction cosines of the line are,
<l,m,n>=<1,2,2>
and equation of plane is 2x−y+√pz+4=0
Direction cosines of the plane are,
<a,b,c>=<2,−1,√p>
Also given,sin‌θ=‌

1

3

On squaring both sides, we get
‌

1

9

=‌

4

9

×‌

p

(p+5)

⇒p+5=4p⇒3p=5⇒p=‌

5

3