A Mathematical Blog

(Note : please patiently allow all 3D applets to load. Depending on your internet speed, the page might take a little longer to load. Also, with dark mode on, you might not be able to see math equations in some browsers.) I have already talked about direction angles in great detail in my previous post. If you are here to read about the essentials I’ll suggest you should read my previous post.  In this short post I want to show you a neat little visualisation, something which, despite my best efforts, I couldn't squeeze into earlier post. I’ll intend to keep it short and to the point as possible, because I have already written a great deal about direction angles. So let’s get straight to it. Firstly, let me state the definition(sort of). Direction angles of a vector are the three angles made by the vector with positive arms of X, Y and Z axes.  Direction Angles of   :   60°, 45 ° , 60 °           \(\vec{u}\...

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...