Question

If the d.rs of $OA$ and $OB$ are $1,-1,-1$ and $2,-1,1$, then the d.cs of the line perpendicular to both $OA$ and $OB$ are

• A. $0,1,-1$
• B. $-2,-3,1$
• C. $\frac{-2}{\sqrt{14}},\frac{-3}{\sqrt{14}},\frac{1}{\sqrt{14}}$
• D. $\frac{2}{\sqrt{41}},\frac{3}{\sqrt{41}},\frac{-1}{\sqrt{41}}$

Answer 1

The correct option is C

$\frac{-2}{\sqrt{14}},\frac{-3}{\sqrt{14}},\frac{1}{\sqrt{14}}$

The Directionsratios of $OA$ will be,
$(\frac{1}{\sqrt{3}},\frac{-1}{\sqrt{3}},\frac{-1}{\sqrt{3}})$
The Direction cosines of $OB$ will be,
$(\frac{2}{\sqrt{6}},\frac{-1}{\sqrt{6}},\frac{1}{\sqrt{6}})$
Now the lines should be such that the product of Dcs will be $0$.
This is only satisfied by Option C