KEAM 2015 Math Paper

Let the equation of line be r=a+λb2 since, line passes through A, so a=4

∧

i

+2

∧

j

+2

∧

k

and line is parallel to the vector 2

∧

i

+3j+6

∧

k

so b=2

∧

i

+3

∧

j

+6

∧

k

Hence, equation of the line is
Distance of point B from the line
=|‌

|(a2−a1)×b|

|b|

|
a2−a1=3

∧

i

+0

∧

j

+0

∧

k

|(a2−a1)×b|=√(−18)2+(9)2
=√405=9√5
|b|=√4+9+36=7
Required distance =‌

9√5

7