Question

The direction cosines of the normal to the plane $2x+3y-6z=5$ are

• A. $(2,3,-6)$
• B. $(\frac{2}{7},\frac{3}{7},-\frac{6}{7})$
• C. $(\frac{2}{5},\frac{3}{5},-\frac{6}{5})$
• D. None of these

Answer 1

Answer: (B)

$(\frac{2}{7},\frac{3}{7},-\frac{6}{7})$

Plane $\Rightarrow 2x+3y-6z=5$

Comparing with $ax+by+cz=d$

$a=2$, $b=3$, $c=-6$, $d=5$

$\sqrt{a^2+b^2+c^2}=\sqrt{4+9+36}=\sqrt{49}=7$

Direction cosines of normal to plane,

$l=\frac{a}{\sqrt{a^2+b^2+c^2}}$, $l=\frac{2}{7}$

$m=\frac{b}{\sqrt{a^2+b^2+c^2}}$, $m=\frac{3}{7}$

$n=\frac{c}{\sqrt{a^2+b^2+c^2}}$, $n=\frac{-6}{7}$

$\therefore (l,m,n)=(\frac{2}{7},\frac{3}{7},\frac{6}{7})$.