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.

Engineering

Mathematics

theorem in space

Section Formulae and Centres of a Triangle

Distance from a Plane

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.

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[A] P = (6,8,10)

Q = (3,4,8)

P₁ = X = 6	¹P₁X = 3
P₂ = Y = 8	¹P₂X = 4
P₃ = Z = 10	¹P₃X = 8

SO,

ℓ = 6 – 3 = 3

b = 8 – 4 = 4

h = 10 – 8 = 2

diagonal

= \sqrt{ℓ^{2} + b^{2} + h^{2}}

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

= \sqrt{9 + 16 + 4}

= \sqrt{29}