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

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

Unit 13.2 Worked Example 3

Unit 13.2 Worked Example 3

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