Page 90 - 35Linear Algebra

90 Vectors in Space, n-Vectors

100
Example 49 of the dot product of two vectors from R .
   
1 1
2 1
   
   
1
 3    1
  ·   = 1 + 2 + 3 + · · · + 100 = .100.101 = 5050.
  
4 1

    2
 .   .
.
.
 .   .
100 1
The sum above is the one Gauß, according to legend, could do in kindergarten.
Definition The length (or norm or magnitude) of an n-vector v is
√
kvk := v v .

101
Example 50 of the norm of a vector from R .



1

 2 
v

 
u 101

 3 
uX p
2

 
= t i = 37, 961.

4



 
i=1

 . 
.

 . 

101
Definition The angle θ between two vectors is determined by the formula
u v = kukkvk cos θ .
101
Example 51 of an angle between two vectors form R .
   
1 1
0
 2   
   
1
 3   
 
  and   is arccos √ 10,201 √ .

4 0 37,916 51
The angle between 
   
 .   .
. .
 .   .
101 1
Definition Two vectors are orthogonal (or perpendicular) if their dot
product is zero.
90