Question

The direction ratios of a normal to the plane $OAB$ where $O=(0,0,0),A=(-1,2,3)$ and $B=(-3,4,5)$ are

• A. $1,2,-1$
• B. $2,1,-1$
• C. $1,1,2$
• D. $1,-1,2$

Answer 1

The correct option is A $1,2,-1$

Let $O(0,0,0)$ ,$A(-1,2,3)$ and $B(-3,4,5)$ be any three points on a plane.
First we find the dr's of a lines joining these points.
Dr's of $OA=(-1,2,3)$
Dr's of $OB=(-3,4,5)$
A normal to this plane will be a line that is normal to both $OA$ and $OB$.
Thus it can be obtained by doing the cross product of $OA$ with $OB$.
Suppose, the normal to the plane is $n$.
Then $n$ = $OA\times OB$
Hence, $n$=$-2i-4j+2k$
The dr's of the normal to the plane are $1,2,-1$.