Question

A parallelepiped is formed by planes drawn through the points $P(6,8,10)$ and $Q(3,4,8)$ parallel to the coordinate planes. Find the length of edges and diagonals of the parallelepiped.

Answer 1

P=(6,8,10)

Q=(3,4,8)

$P^1=x=6$ $P_1^{1}x=3$

$P^2=y=8$ $P_2^{1}y=4$

$P^3=z=10$ $P_3^1=z=8$

SO,

l=6-3=3

b=8-4=4

h=10-8=2

diagonal =$\sqrt{l^2+b^2+b^2}$

=$\sqrt{3^2+4^2+2^2}$

=$\sqrt{9+16+4}$

=$\sqrt{29}$