Find the exact shortest distance of the point $A\left( 3,1,-2 \right)$ to the plane \({{p}_{1}}:x-

Question

Find the exact shortest distance of the point $A\left( 3,1,-2 \right)$ to the plane ${{p}_{1}}:x-3y+2z=-5$. Find the coordinates of foot of perpendicular of point $B\left( 7,4,-5 \right)$ to plane ${{p}_{1}}:x-3y+2z=-5$.

Accepted Answer

(i) $\frac{1}{\sqrt{14}}$units (ii) $\left( \frac{54}{7},\frac{13}{7},-\frac{25}{7} \right)$

Vectors - Distance from a Point to a Plane

Vectors - Distance from a Point to a Plane

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