March 26, 2021

Chapters

- Exercise 1
- Exercise 2
- Exercise 3
- Exercise 4
- Exercise 5
- Exercise 6
- Exercise 7
- Exercise 8
- Exercise 9
- Solution of exercise 1
- Solution of exercise 2
- Solution of exercise 3
- Solution of exercise 4
- Solution of exercise 5
- Solution of exercise 6
- Solution of exercise 7
- Solution of exercise 8
- Solution of exercise 9

## Exercise 1

Calculate the head of the vector knowing that its components are and its tail is .

## Exercise 2

Given points and , calculate the value of **a** if the magnitude of the vector is one.

## Exercise 3

Normalize the vectors: and .

## Exercise 4

Determine the unit vector, , which is in the same direction as the vector .

## Exercise 5

Calculate the coordinates of D so that the quadrilateral formed by the vertices: and D; is a parallelogram.

## Exercise 6

The vectors and form a basis. Express this in basis the vector .

## Exercise 7

Find the value of **k** so that the angle that forms between and is:

1

2

3

## Exercise 8

Calculate the value of **a** so that the vectors and form an angle of .

## Exercise 9

If is an orthonormal basis, calculate:

1

2

3

4

## Solution of exercise 1

Calculate the head of the vector knowing that its components are and its tail is .

## Solution of exercise 2

Given points and , calculate the value of **a** if the magnitude of the vector is one.

## Solution of exercise 3

Normalize the vectors: and .

## Solution of exercise 4

Determine the unit vector, , which is in the same direction as the vector .

## Solution of exercise 5

Calculate the coordinates of D so that the quadrilateral formed by the vertices: and D; is a parallelogram.

Hence,

## Solution of exercise 6

The vectors and form a basis. Express this in basis the vector .

Replacing the value of **a** in the second equation:

Plugging the value of b in the first equation:

## Solution of exercise 7

Find the value of **k** so that the angle that forms between and is:

1

2

3

After solving the above equation:

## Solution of exercise 8

Calculate the value of **a** so that the vectors and form an angle of .

## Solution of exercise 9

If is an orthonormal basis, calculate:

1

2

3

4