Question

The direction ratios of a normal to the plane passing through $(0,1,0)$ , which makes an angle $\left(\frac{\pi }{4}\right)$ with the plane $x+y=3$, are

• A. $1,\sqrt{2},1$
• B. $1,1,\sqrt{2}$
• C. $1,1,2$
• D. $\sqrt{2},1,1$

Answer 1

Answer: (B)

$1,1,\sqrt{2}$

Direction ratios of normal to the plane $x+y=3$ are $(1,1,0)$

Let the direction ratios of normal to the other plane be $(a,b,c)$

Since, angle between them is ${45}^{\circ },$

$\frac{a+b}{\sqrt{2}\sqrt{a^2+b^2+c^2}}=\frac{1}{\sqrt{2}}$

On solving, we get,

$2ab=c^2$

Only $(1,1,\sqrt{2})$ satisfies this relation.

So, Option (B)