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Vectors and Lines

Kaitlin McNeil Inglés 16 fichas

Fichas del conjunto (16)

1length of vectorsqrt(x^2+y^2+z^2)
2If v and w are non-zero vectors in R3 when doesif and only if v and w have the same length and direction
3Geometric Vectorsthe line segment from a point to another, the length and direction are what is important not the location.
4The Parallelogram LawIn the parallelogram determined by two vectors v and w, the vector v+w is the diagonal with the same tail a v and w.
5Scalar Multiplication LawIf 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
6The vector equation of a linep=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
7Parametric Equation of a LineThe 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
8v•v=?||V||^2
9v•w=w•v
10(kv)•wk(w•v) fora all scalars k
11u•(v±w)u•v±u•w
12||v|| ||w|| cos◊v•w
13two vectors are orthogonal ifv•w=0 or the angle btw them is π/2
14The projection of u on dprojd u = u•d/||d||^2 d
15the vector u - projd u is...orthogonal to d
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