Direction Cosine | Superprof

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Example

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 $\text{[math]}$ are:

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$ $\text{[math]}$

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 $\text{[math]}$ .

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$

$\text{[math]}$

A vector $\text{[math]}$ is drawn on the basis of orthonormal and has components $\text{[math]}$ . Find the direction cosines.

$\text{[math]}$ $\text{[math]}$ $\text{[math]}$

$\text{[math]}$

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