# Ques: Find the unit vector which is perpendicular to the resultant of 2i+3j+5k and -i+2j+7k ; and passes through (1,2,4)

Arun Kumar IIT Delhi
8 years ago
$v_{res}=(2\vec i +3 \vec j+5\vec k)+(-\vec i +2 \vec j +7\vec k)=2\vec i+5\vec j+12j\\ v_{along\,v_{res}\,and\,passing\,through \,v_{1}}=(2\vec i +3 \vec j+5\vec k)+t(\vec i+5\vec j+12j)$
Assume a point x,y,z on the require unit vector line
$(x,y,z).(1,5,12)=z+5y+12=0$
this cut that line at
$(2+t)+5(3+5t)+12(5+12t)=0$
get t from here now you got that point.
Now
$v_{required}=x\vec i+y\vec j+z\vec k+t(\vec i+2\vec j+4\vec k) \\=>\widehat{n_{required}}=v_{required}/|v_{required}|$

Arun Kumar
IIT Delhi