Question

The distance between $(2,1,0)$ and $2x+y+2z+5=0$ is

• A. 10
• B. 10/3
• C. 10/9
• D. 5
• E. 1

Answer 1

Answer: (B)

The distance of a point $\left(x_1,y_1,z_1\right)$ from the plane $ax+by+cz+d=0$ is given by
$=\left|\frac{a{x}_1+b{y}_1+c{z}_1+d}{\sqrt{a^2+b^2+c^2}}\right|$
$\therefore$ Distance of the point $(2,1,0)$ from the plane $2x+y+2z+5=0$ is equal to
$=\left|\frac{2\times 2+1\times 1+2\times 0+5}{\sqrt{(2{)}^2+(1{)}^2+(2{)}^2}}\right|=\left|\frac{4+1+5}{\sqrt{4+1+4}}\right|=\frac{10}{3}$