Question

The direction ratios of two lines are 1,-3, 4 and -2, 0, 6. The direction cosines of a line perpendicular to both the lines are

Answer 1

Direction ratio of $1^{st}$ line is 1, -3, 4
direction ratio of $2^{nd}$ line is -2, 0, 6
so direction ratio of line perpendicular to both is cross product of direction ratio of $1^{st}$ & $2^{nd}$ line $=$
$\left|\begin{array}{ccc}i& J& K\\ 1& -3& 4\\ -2& 0& 6\end{array}\right|=\widehat{(}-18)-\hat{j}(14)+K(-6)$
& the direction cosine is $(\frac{-18}{\sqrt{(-18{)}^2+(-14{)}^2+(-6{)}^2}},\frac{-14}{\sqrt{(-18{)}^2+(-14{)}^2+(-6{)}^2}},\frac{-6}{\sqrt{(-18{)}^2+(-14{)}^2+(-6{)}^2}})$