The document contains notes from a civil engineering student's second semester studying vector calculus concepts. It includes examples of [1] defining vectors, [2] calculating the dot product of two vectors, and [3] representing a line as a vector function dependent on a parameter t. Formulas shown include vector addition and subtraction, as well as parametric, vector, and cartesian representations of lines.

1. GEOVANNI CONTRERAS GARCÍA
2DO SEMESTRE
ING. CIVIL

3. A=(2,3,4) l=v3+t(2,3,4)
u=(2,0,6) v3=v1·v2 2 0 6 =(0i)+(0j)+(2-18k)
V=(3,0,1) 3 0 1
l=0,0,-16+t (2,3,4)
x=0+2t y=0+3t z=-16+4t

4. Forma vectorial Forma Continua
(1,3,-2)-(2,3,4) x2=1 y2=3
a=(-1,0,-6) x2-x1=1 y2-y1=0
x1=0 y1=3
z2=-2
Forma paramétrica z2-z1=-6
r= (1,3,-2)+t(-1,0,-6) z1=4
X=1+t ; y=3 z=-2-6t

7. a=(1,2,3) V3=V1·V2 2 -1 5
u=(2,-1,5) 3 2 4 =(-4-10)i-(8-15)j+(4+3)k
v=(3,2,4)
l=V3+t(1,2,3)
l=(-14+t)+t(1,2,3)
x=-14+t y=7+2t z=7+3t