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Let $\mathrm{A}, \mathrm{B}, \mathrm{C}$ be the feet of perpendiculars from a point $\mathrm{P}$ on the $x y, y z$ and zx planes respectively. Find the coordinates of $\mathrm{A}, \mathrm{B}, \mathrm{C}$ in each of the following where the point $P$ is
(i) $(3,4,5)$
(ii) $(-5,3,7)$
(iii) $4,-3,-5)$
(i) $(3,4,5)$
(ii) $(-5,3,7)$
(iii) $4,-3,-5)$
Solution:
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Verified Answer
(i) $(3,4,5)$
Coordinates of $\mathrm{A}$ from a point $\mathrm{P}$ on xy plane $=(3,4,0)$ Coordinates of $\mathrm{B}$ from a point $\mathrm{P}$ on $\mathrm{yz}$ plane $=(0,4,5)$
Coordinates of $\mathrm{C}$ from a point $\mathrm{P}$ on zx plane $=(3,0,5)$
(ii) $(-5,3,7)$
Coordinates of A from a point $\mathrm{P}$ on xy plane $=(-5,3,0)$
Coordinates of $\mathrm{B}$ from a point $\mathrm{P}$ on $\mathrm{yz}$ plane $=(0,3,7)$
Coordinates of $\mathrm{C}$ from a point $\mathrm{P}$ on zx plane $=(-5,0,7)$
(iii) $(4,-3,-5)$
Coordinates of A from a point $\mathrm{P}$ on xy plane $=(4,-3,0)$
Coordinates of $\mathrm{B}$ from a point $\mathrm{P}$ on $\mathrm{yz}$ plane $=(0,-3,-5)$
$$
\text { Coordinates of } \mathrm{C} \text { from a point } \mathrm{P} \text { on } \mathrm{zx} \text { plane }=(4,0,-5)
$$
Coordinates of $\mathrm{A}$ from a point $\mathrm{P}$ on xy plane $=(3,4,0)$ Coordinates of $\mathrm{B}$ from a point $\mathrm{P}$ on $\mathrm{yz}$ plane $=(0,4,5)$
Coordinates of $\mathrm{C}$ from a point $\mathrm{P}$ on zx plane $=(3,0,5)$
(ii) $(-5,3,7)$
Coordinates of A from a point $\mathrm{P}$ on xy plane $=(-5,3,0)$
Coordinates of $\mathrm{B}$ from a point $\mathrm{P}$ on $\mathrm{yz}$ plane $=(0,3,7)$
Coordinates of $\mathrm{C}$ from a point $\mathrm{P}$ on zx plane $=(-5,0,7)$
(iii) $(4,-3,-5)$
Coordinates of A from a point $\mathrm{P}$ on xy plane $=(4,-3,0)$
Coordinates of $\mathrm{B}$ from a point $\mathrm{P}$ on $\mathrm{yz}$ plane $=(0,-3,-5)$
$$
\text { Coordinates of } \mathrm{C} \text { from a point } \mathrm{P} \text { on } \mathrm{zx} \text { plane }=(4,0,-5)
$$
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