Question

What is the distance of the plane $2x+y+2z=3$ from the origin?

• A. $1$ unit
• B. $1.5$ units
• C. $2$ units
• D. $2.5$ units

Answer 1

The correct option is A $1$ unit

Distance of a point $(m,n,o)$ from a plane $ax+by+cz+d=0$ is,

$\frac{|am+bn+zo+d|}{\sqrt{a^2+b^2+c^2}}$

Here the point is $(0,0,0)$. So, the required distance is,

$\frac{\left|2\right(0)+1(0)+2(0)-3|}{\sqrt{2^2+1^2+2^2}}=\frac{3}{3}=1$

Hence, A is correct.