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Paolo
5
5 (63 reviews)
Paolo
£30
/h
Gift icon
1st lesson free!
Hiren
5
5 (23 reviews)
Hiren
£150
/h
Gift icon
1st lesson free!
Akash
5
5 (58 reviews)
Akash
£45
/h
Gift icon
1st lesson free!
Sehaj
4.9
4.9 (47 reviews)
Sehaj
£40
/h
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1st lesson free!
Luke
5
5 (76 reviews)
Luke
£125
/h
Gift icon
1st lesson free!
Johann
5
5 (35 reviews)
Johann
£35
/h
Gift icon
1st lesson free!
Intasar
5
5 (48 reviews)
Intasar
£79
/h
Gift icon
1st lesson free!
Harinder
5
5 (36 reviews)
Harinder
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Let's go

Exercise 1

Find two unit vectors for and and determine the orthogonal vector for the two.

Exercise 2

Find a unit vector that is perpendicular to and .

Exercise 3

Given the vectors and , find the product and verify that this vector is orthogonal to and . Also, find the vector and compare it with .

Exercise 4

Consider the following figure:

Determine:

1 The coordinates of D if ABCD is a parallelogram.

2 The area of the parallelogram.

Exercise 5

Given the points and , determine:

1 What values of a are collinear.

2 Determine if values exist for a so that A, B, and C are three vertices of a parallelogram of area . If values do exist, determine the coordinates of C:

Exercise 6

and are the three vertices of a triangle.

1. Calculate the cosine of each of the three angles in the triangle.

2. Calculate the area of the triangle.

 

 

Solution of exercise 1

Find two unit vectors for and and determine the orthogonal vector for the two.

 

 

Solution of exercise 2

Find a unit vector that is perpendicular to and .

 

Solution of exercise 3

Given the vectors and , find the product and verify that this vector is orthogonal to and . Also, find the vector and compare it with .

 

 

Solution of exercise 4

Consider the following figure:

Determine:

1 The coordinates of D if ABCD is a parallelogram.

 

 

2 The area of the parallelogram.

 

Solution of exercise 5

Given the points and , determine:

1 What values of a are collinear.

If A, B, and C are collinear, the vectors and  are linearly dependent and have proportional components.

 

2 Determine if values exist for a so that A, B, and C are three vertices of a parallelogram of area . If values do exist, determine the coordinates of C:

Find various Maths tutors near me on Superprof.

 

Solution of exercise 6

and are the three vertices of a triangle.

1. Calculate the cosine of each of the three angles in the triangle.

 

2. Calculate the area of the triangle.

 

 

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Emma

Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.