Question

A plane is at a distance of 8 units from the origin and it is normal to the line having direction ratios 2,1,2. The equation of this plane is .

• A. x + 2y + z = 24
• B. 2x + y + 2z = 24
• C. 2x + 2y + z = 72
• D. x + 2y + 2z = 72

Answer 1

The correct option is B 2x + y + 2z = 24

We’ll calculate direction cosines of normal first which will be - $\frac{2}{\sqrt{2^2+1^1+2^2}},\frac{1}{\sqrt{2^2+1^1+2^2}},\frac{2}{\sqrt{2^2+1^1+2^2}}$ Or $\frac{2}{3},\frac{1}{3},\frac{2}{3}$

So now we know l , m and n and “d” is already given in the question. The equation of line will be
$\frac{2}{3}x+\frac{1}{3}y+\frac{2}{3}z=8$

Or 2x + y + 2z = 24