Exercise 1
Given the vectors 
and 
, calculate the following:
1. 
2. 
3. 
4. 
5. 
Exercise 2
For what values of a do the vectors 
and 
form a basis?
Exercise 3
Determining the value of the coefficient k for the vectors 
if the vectors are:
1. Orthogonal.
2. Parallel.
Exercise 4
Find the direction cosines of the vector 
.
Exercise 5
Calculate the angle between the vectors 
and 
.
Exercise 6
Given the vectors 
and 
, calculate:
1 The magnitudes of 
and 
·
2 The cross product of and ·
3 The unit vectororthogonal to and ·
4 The area of the parallelogram whose sides are the vectors and ·
Exercise 7
Calculate the triple product of: 
if 
.
Exercise 8
Given the vectors 
, and 
, calculate the triple product 
. Also, what is the volume of the parallelepiped whose edges are formed by these vectors?
Solution of exercise 1
Given the vectors and , calculate the following:
1.
2.
3.
4.
5.
Solution of exercise 2
For what values of a do the vectors and form a basis?
For 
, the vectors form a basis.
Solution of exercise 3
Determining the value of the coefficient k for the vectors if the vectors are:
1. Orthogonal.
2. Parallel.
The system does not have a solution.
Solution of exercise 4
Find the direction cosines of the vector .
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Solution of exercise 5
Calculate the angle between the vectors and .
Solution of exercise 6
Given the vectors and , calculate:
1 The magnitudes of and ·
2 The cross product of and ·
3 The unit vectororthogonal to and ·
4 The area of the parallelogram whose sides are the vectors and ·
Solution of exercise 7
Calculate the triple product of: if .
Solution of exercise 8
Given the vectors , and , calculate the triple product . Also, what is the volume of the parallelepiped whose edges are formed by these vectors?
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