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Home » Engineering Mechanics » Principles of Statics » Components of a Force
003 Components of a 3D force with given distances
Problem 003
Which of the following correctly defines the 500 N force that passes from A(4, 0, 3) to B(0, 6, 0)?
A. 256i - 384j + 192k N
B. -256i + 384j - 192k N
C. -384i + 192j - 256k N
D. 384i - 192j + 256k N
Solution 003
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From the figure
rAB = −4i + 6j − 3k m
Unit vector from A to B:
rAB
λAB =
rAB
−4i + 6j − 3k
λAB =
−−−−−−−−−−−−−−−
2
√ (−4)2 + 6 + (−3)
2
λAB = −0.5121i + 0.7682j − 0.3841k
Rectangular representation of F:
F = F λAB
F = 500(−0.5121i + 0.7682j − 0.3841k)
F = −256i + 384j − 192k N
Answer: B
Calculator Technique
Click here to show or hide the solution
May work in the following CASIO models: fx-570ES, fx-570ES Plus, fx-115ES, fx-115ES Plus, fx-991ES, and fx-991ES Plus
Use VECTOR mode: [MODE] → 8:VECTOR
This mode is made primarily for vector quantities, thus, handling forces in 3D is straightforward.
Enter position vector:
[MODE] → 8:VECTOR → 1:VctA → 1:3
r = VctA = [ -4 6 -3 ]
Solve for vector F: AC
F = 500[×]([SHIFT] → [5 VECTOR] → 3:VctA ÷ [SHIFT] → [hyp Abs]( → [SHIFT] → [5 VECTOR] → 3:VctA) ) =
Calculator display: 500×(VctA÷Abs(VctA))
F = [ -256 384 -192 ] answer
Note: the unit vector λ is:
λ = [SHIFT] → [5 VECTOR] → 3:VctA ÷ [SHIFT] → [hyp Abs]( → [SHIFT] → [5 VECTOR] → 3:VctA)
Tags:
components of a force 3D Force X-Component Y-component Vector Notation Z-Component of a Force Unit Vector
CalTech
‹ 002 Components of forces with given slope up 004 Components of a 3D force with given angles ›
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MATHalino - Engineering Mathematics • Copyright 2020 © Jhun Vert • All rights reserved
Engineering Mechanics
Principles of Statics
Components of a Force
001 Horizontal and vertical componets of planar forces
002 Components of forces with given slope
003 Components of a 3D force with given distances
004 Components of a 3D force with given angles
005 Components of a force in rotated axes
006 Components of a force in axes that are not perpendicular to each other
007 Components of a force parallel and perpendicular to the incline
008 Components of a force at different pairs of axes
009 Force with given component parallel to the incline
010 Components of force normal and tangent to hypotenuse of a triangle
016 Components of a force parallel to supporting bars
017 Computation of force with given component parallel to a frame member
Moment of a Force
Couples
Resultant of Concurrent Force System
Resultant of Parallel Force System
Resultant of Non-Concurrent Force System
Equilibrium of Force System
Analysis of Structures
Friction
Centroids and Centers of Gravity
Moment of Inertia and Radius of Gyration
Dynamics
Force Systems in Space
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