Question

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

• A. $5,-3,3$
• B. $\frac{5}{\sqrt{43}},\frac{-3}{\sqrt{43}},\frac{3}{\sqrt{43}}$
• C. $\frac{1}{2},\frac{-3}{10},\frac{3}{10}$
• D. $1,\frac{-3}{5},\frac{3}{5}$

Answer 1

The correct option is B $\frac{5}{\sqrt{43}},\frac{-3}{\sqrt{43}},\frac{3}{\sqrt{43}}$

Given plane is, $5(x-2)=3(y-z)$
$\Rightarrow 5x-3y+3z-10=0$
So direction ratios of normal to the plane are $5,-3$ and $3$.
Thus direction cosines are, $\frac{5}{\sqrt{5^2+3^2+3^2}},-\frac{3}{\sqrt{5^2+3^2+3^2}},\frac{3}{\sqrt{5^2+3^2+3^2}}$
or $\frac{5}{\sqrt{43}},\frac{-3}{\sqrt{43}},\frac{3}{\sqrt{43}}$