Find the shortest distance from the point $( 2,0 , - 3 )$ to the plane $x + y + z = 1$.
Select the correct answer.
A) $D = \sqrt { 61 }$
B) $D = 106$
C) $D = 1.15$
D) $D = 90$
E) $D = 61$

Question

Quizplus · Accepted Answer

We use the formula for the distance of a point to a plane, which is given by $\frac{Ax_0+By_0+Cz_0+D}{\sqrt{A^2+B^2+C^2}}$, where $(x_0,y_0,z_0)$ is the point and $Ax+By+Cz+D=0$ is the equation of the plane. In this case, the plane is $x+y+z=1$, so $A=B=C=1$ and $D=-1$. Plugging in the given point, we get $$\frac{2+0-3-1}{\sqrt{1^2+1^2+1^2}}=-\frac{2}{\sqrt{3}}$$ which is approximately $-1.15$ in decimal form. The distance is the absolute value of this, so the answer is $D=1.15$.

Find the Shortest Distance from the Point (2,0,−3)( 2,0 , - 3 )(2,0,−3)

Find the Shortest Distance from the Point $( 2,0 , - 3 )$