Direction Angles & Direction Cosines
Direction of a Vector in 3D My previous post was about two primary ways in which we can describe the direction of a vector in two dimensional space. In this post, we will add in a third dimension(Z-axis) and discuss about a number of titles that are used to describe the direction of a vector in three dimensional space. Let’s take an example of a vector in 3D in component form, \(\vec{u} = 2\hat{i} + \frac{4}{\sqrt{2}} \hat{j} + 2\hat{k}\) Just like for a 2D vector, the scalar components of a 3D vector can tell us the direction of the vector in the coordinate system. From the origin, we go 2 units in the positive X-direction; take a right angle turn and travel \(\frac{4}{\sqrt{2}}\) units(about 2.8 units) in the positive Y-direction; and finally travel 2 units in the positive Z-direction. The arrow drawn from the start(origin) to the end points us in the direction of \(\vec{u}\). So a description that properly describes the direction(& magnitude) of \(\vec{u}\) co...