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.

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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.

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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.