Let us compute the dot product and magnitudes of both vectors.īy using the angle between two vectors formula using dot product, θ = cos -1 [ ( a Let us find the angle between vectors using both dot product and cross product and let us see what is the ambiguity that a cross product can cause.Īngle Between Vectors in 2D Using Dot Product Let us consider two vectors in 2D say a = and b =. Let us also see the ambiguity caused by the cross-product formula to find the angle between two vectors. Let us see some examples of finding the angle between two vectors using dot product in both 2D and 3D. Here, sin -1 is read as "sin inverse" and it is called " inverse sine function".
![rotation rules 90 geometry rotation rules 90 geometry](https://image1.slideserve.com/3226347/slide11-l.jpg)
This formula causes some ambiguity (which we discuss in the next section) and is not a popular formula to use to find angle between vectors. This is is the formula for the vector angle in terms of the cross product (vector product). Angle Between Two Vectors Using Cross Productīy the definition of cross product, a × b = | a| | b| sin θ \(\hat\) is a unit vector and hence its magnitude is 1. Here, cos -1 is read as "cos inverse" and it is called " inverse cosine function". This is is the formula for the angle between two vectors in terms of the dot product (scalar product). Note that the cross-product formula involves the magnitude in the numerator as well whereas the dot-product formula doesn't.Īngle Between Two Vectors Using Dot Product
![rotation rules 90 geometry rotation rules 90 geometry](https://www.onlinemath4all.com/images/90degreeclockwiserotation5.png)
That point P was rotated about the origin (0,0) by 60 degrees. I included some other materials so you can also check it out. There are many different explains, but above is what I searched for and I believe should be the answer to your question. There is also a system where positive degree is clockwise and negative degree anti-clockwise, but it isn't widely used.
![rotation rules 90 geometry rotation rules 90 geometry](http://systry.com/wp-content/uploads/2016/10/Rotations-Doodle-Notes.png)
Product of unit vector in X direction with that in the Y direction has to be the unit vector in the Z direction (coming towards us from the origin). Clockwise for negative degree.įor your second question, it is mainly a conventional that mathematicians determined a long time ago for easier calculation in various aspects such as vectors.