June 26, 2019

Chapters

## 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 vector orthogonal 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 .

## 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 vector orthogonal 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?