Vectors and Lines

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review for test 4 chp 4.1
Kaitlin McNeil
Flashcards by Kaitlin McNeil, updated more than 1 year ago
Kaitlin McNeil
Created by Kaitlin McNeil almost 9 years ago
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Question Answer
length of vector sqrt(x^2+y^2+z^2)
If v and w are non-zero vectors in R3 when does if and only if v and w have the same length and direction
Geometric Vectors the line segment from a point to another, the length and direction are what is important not the location.
The Parallelogram Law In the parallelogram determined by two vectors v and w, the vector v+w is the diagonal with the same tail a v and w.
Scalar Multiplication Law If a is a real number and v is a non-zero vector then the length if av is |a|||v|| and the direction is opposite iff a<0
The vector equation of a line p=p0+td where t is any scalar ie. the point p is on this line if a real number t exists st p=p0+td
Parametric Equation of a Line The line through P0(x0,y0,z0) with direction vector d=(a,b,c)≠0 is given by x=xo+ta y=yo+tb z=zo+tc t is any scalar
v•v=? ||V||^2
v•w= w•v
(kv)•w k(w•v) fora all scalars k
u•(v±w) u•v±u•w
||v|| ||w|| cos◊ v•w
two vectors are orthogonal if v•w=0 or the angle btw them is π/2
The projection of u on d projd u = u•d/||d||^2 d
the vector u - projd u is... orthogonal to d
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