Distance of lines

Find the distance of lines AE, CG in cuboid ABCDEFGH, if given | AB | = 3cm, | AD | = 2 cm, | AE | = 4cm

Result

x =  4.472 cm

Solution:

a=3 cm b=2 cm c=4 cm  u1=b2+c2=22+42=2 5 cm≐4.4721 cm u2=a2+u12=32+4.47212=29 cm≐5.3852 cm  x=u1=4.4721=2 5≐4.4721=4.472  cm a = 3 \ cm \ \\ b = 2 \ cm \ \\ c = 4 \ cm \ \\ \ \\ u_{ 1 } = \sqrt{ b^2+c^2 } = \sqrt{ 2^2+4^2 } = 2 \ \sqrt{ 5 } \ cm \doteq 4.4721 \ cm \ \\ u_{ 2 } = \sqrt{ a^2 + u_{ 1 }^2 } = \sqrt{ 3^2 + 4.4721^2 } = \sqrt{ 29 } \ cm \doteq 5.3852 \ cm \ \\ \ \\ x = u_{ 1 } = 4.4721 = 2 \ \sqrt{ 5 } \doteq 4.4721 = 4.472 \ \text{ cm }

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