Chapters

## Exercise 1

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

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Jamie
£25
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1st lesson free!
4.9 (7 reviews)
Dr. Kritaphat
£49
/h
1st lesson free!
5 (15 reviews)
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## 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

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