Wize University Physics Textbook (Master) > Force Vectors (Advanced Info)
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.
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