Question

If the d.rs of two lines are $1,-2,3$ and $2,0,1$, then the d.rs of the line perpendicular to both the given lines is

• A. $-2,5,4$
• B. $2,-5,4$
• C. $2,5,-4$
• D. $1,5,-4$

Answer 1

The correct option is A $-2,5,4$

$OA$ and $OB$ are given by $(1,-2,3),(2,0,1)$.
A line that will be perpendicular to both $OA$ and $OB$ can be obtained by doing the cross product of $OA$ with $OB$.

Then, $n=OA\times OB$
Hence, $n=-2i+5j+4k$
Hence, the dr's are $(-2,5,4)$.