What do you get when you cross a mountain climber with a mosquito? Nothing—you can’t cross a scalar with a vector!
But what do you get when you cross two vectors? Wolfram|Alpha can tell you. For example:
And in fact, Wolfram|Alpha can give lots of information on vectors. A vector is commonly defined as a quantity with both magnitude and direction and is often represented as an arrow. The direction of the arrow matches the direction of the vector, while the length represents the magnitude of the vector. Wolfram|Alpha can now plot vectors with this arrow representation in 2D and 3D and return many other properties of the vector.
Suppose you know only the point in R^n corresponding to your vector and you want to know its magnitude and direction. You can query Wolfram|Alpha for the vector’s length to find its magnitude:
And to find the direction, you can ask for the angles between the vector and the coordinate axes:
If you want to find both the magnitude and direction, you can represent the vector in polar or spherical coordinates. The radius gives you the magnitude of your vector, while the angles specify its direction.
Wolfram|Alpha can even help you add and subtract two vectors using the tip-to-tail method.
So whether your studies are in algebra, calculus, or physics, Wolfram|Alpha can be your resource for learning about vectors.