Wize University Statics Textbook (Master) > Force Vectors

Things to know about Vectors - Building & Manipulation

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FORCE VECTORS - How they may be presented or shown in a problem:
 Given in Cartesian Vector Form (ex:  F = [ 3i + 7j - 10l ] N..  
THIS IS THE BEST as it's ready to use!
Given as a magnitude with two points (or a starting point and point it acts through)
build the position vector between the points (remember FROM the starting point TO the 2nd point)
then find the magnitude (square-root of the squares of the components)
unit vector = position vector / magnitude
build the Force vector:  Fvector = Fmagnitude  u
 Given Direction Cosine Angles   α, β, ϒ
make sure they truly ARE direction cosine angles - they must measure from the positive x, y, or z axis TO the line of action of the force vector
if only given 2 of the 3 angles, use the cos^2 identity to calculate the 3rd missing angle.
then build the unit vector from u = cos(alpha) i + cos(beta) j + cos(gamma)k
lastly, build the force vector from F = F u
Given those shaded / planar triangles
use "cos cos" or "cos sin" depending on where you need to PROJECT the vector
example vector might end up being:   F = Fcos(angle1)cos(angle2)i + Fcos(angle1)sin(angle2)j + Fsin(angle1)
 Given those small 3-4-5 or 5-12-13 triangles on the vector
either find the angle you need to use sin/cos -OR- use the ratio instead of cos(angle), etc.
then build the force vector.

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Other things you should know how to do / deal with:
 How to break down a vector into perpendicular or rectangular components
use: Basic Trigonometric rules, aka. SOH CAH TOA
 How to break down a vector into non-perpendicular component (in non-right triangles)
use: Law of Sine & Law of Cosine
 Projecting a vector along a line
use: Use the dot product
 Finding the angle between two vectors
Modified dot product

Wize University Statics Textbook (Master) > Force Vectors

Things to know about Vectors - Building & Manipulation

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