Chapters

In the case of a vector, direction is one of the most important components. Without direction, you won't call it a vector, that would be a straight line that has magnitude only. We can find the direction of a vector with the help of cosine. In an orthonormal basis, direction cosines of the vector are:

It is necessary that you should be working on an orthonormal basis otherwise this formula won't be valid.

The best Maths tutors available
Sehaj
4.9
4.9 (56 reviews)
Sehaj
£60
/h
Gift icon
1st lesson free!
Intasar
5
5 (68 reviews)
Intasar
£129
/h
Gift icon
1st lesson free!
Johann
5
5 (48 reviews)
Johann
£50
/h
Gift icon
1st lesson free!
Hiren
5
5 (32 reviews)
Hiren
£149
/h
Gift icon
1st lesson free!
Poonam
5
5 (62 reviews)
Poonam
£100
/h
Gift icon
1st lesson free!
Harjinder
4.9
4.9 (163 reviews)
Harjinder
£25
/h
Gift icon
1st lesson free!
Syed
5
5 (65 reviews)
Syed
£50
/h
Gift icon
1st lesson free!
Farooq
4.9
4.9 (50 reviews)
Farooq
£50
/h
Gift icon
1st lesson free!
Sehaj
4.9
4.9 (56 reviews)
Sehaj
£60
/h
Gift icon
1st lesson free!
Intasar
5
5 (68 reviews)
Intasar
£129
/h
Gift icon
1st lesson free!
Johann
5
5 (48 reviews)
Johann
£50
/h
Gift icon
1st lesson free!
Hiren
5
5 (32 reviews)
Hiren
£149
/h
Gift icon
1st lesson free!
Poonam
5
5 (62 reviews)
Poonam
£100
/h
Gift icon
1st lesson free!
Harjinder
4.9
4.9 (163 reviews)
Harjinder
£25
/h
Gift icon
1st lesson free!
Syed
5
5 (65 reviews)
Syed
£50
/h
Gift icon
1st lesson free!
Farooq
4.9
4.9 (50 reviews)
Farooq
£50
/h
Gift icon
1st lesson free!
Let's go

Example

Determine the direction cosines of the vector with components .

A vector is drawn on the basis of orthonormal and has components . Find the direction cosines.

Did you like this article? Rate it!

4.00 (3 rating(s))
Loading...
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.