(a) Explanation Sketch the tetrahedron edge O A is perpendicular to edge B C shown in the Figure 1. Write the equation for the tetrahedron edge O A is perpendicular to edge B C . O A → ⋅ B C → = 0 (I) From the triangle O B C : ( O A ) x = a 2 Here, the length of the side O A along the direction of x axis is a . Refer from the fig 1 for the triangle O B C : tan θ = o p p a d j = ( O A ) z ( O A ) x Rewrite the above relation for ( O A ) z . ( O A ) z = ( O A ) x tan θ (II) Here, the sides of the tetrahedron along x and z is ( O A ) x and ( O A ) z . Substitute a / 2 for ( O A ) x and 30 ° for θ in equation (II). ( O A ) z = a 2 tan 30 ° = a 2 ( 1 3 ) = a 2 3 Write the equation for the tetrahedron edge O A along the co-ordinate axis. O A → = ( O A x ) i + ( O A y ) j ^ + ( O A z ) k ^ (III) Substitute a / 2 for ( O A ) x and a 2 3 for ( O A ) z in equation (III) (b) To determine The perpendicular distance between the edges O A and B C .

VEC MECH 180-DAT EBOOK ACCESS(STAT+DYNA)

12th Edition

ISBN: 9781260916942

Author: BEER

Publisher: MCG

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Chapter 3.2, Problem 3.62P

(a)

To determine

Prove that whether the two opposide edges of tetrahedron are perpendicular to each other.

(b)

To determine

The perpendicular distance between the edges OA and BC.

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Chapter 3.2, Problem 3.61P

Chapter 3.2, Problem 3.63P

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Chapter 3 Solutions

VEC MECH 180-DAT EBOOK ACCESS(STAT+DYNA)

Ch. 3.1 - A foot valve for a pneumatic system is hinged at...Ch. 3.1 - 3.2A foot valve for a pneumatic system is hinged...Ch. 3.1 - It is known that a vertical force of 200 lb is...Ch. 3.1 - A 300-N force is applied at A as shown. Determine...Ch. 3.1 - A 300-N force is applied at A as shown. Determine...Ch. 3.1 - An 8-lb force P is applied to a shift lever....Ch. 3.1 - For the shift lever shown, determine the magnitude...Ch. 3.1 - An 11-lb force P is applied to a shift lever. The...Ch. 3.1 - Rod AB is held in place by the cord AC. Knowing...Ch. 3.1 - Rod AB is held in place by the cord AC. Knowing...

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Prove that whether the two opposide edges of tetrahedron are perpendicular to each other.

Solution Summary: The author demonstrates that the two opposide edges of tetrahedron OA and BC are perpendicular to each other.

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Prove that whether the two opposide edges of tetrahedron are perpendicular to each other.

The perpendicular distance between the edges OA and BC.

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Chapter 3 Solutions