Unit Vector to Verbal Representation

[eggsandbakey]

I'm currently taking my first physics class, and on the very first day, my teacher began discussing vectors as if everyone knew what Unit Vectors were.


I've managed to understand most of his lecture thus far, but I still don't understand- How do you convert from Unit vectors (denoted by i along the x axis, and j along the y axis) to Verbal representation? (My teacher commonly writes things in verbal representation like this: {24 [m] at 65 (degrees) along +x}.


Could anyone help me?


- eggsandbakey

 

[Doc Al]

I've never heard that referred to as the "verbal representation", but that's as good a name as any.

Unit vectors essentially give you the components of a vector along the axes. Can you take that example you gave and find its x and y components?

 

[HallsofIvy]

Unit vectors always have length 1 and these vectors always point in the direction of the axes. What angle do they make with the x-axis?

 

[Astronuc]

The vector provides a 'direction', and the unit (or unity) simply implies that it has magnitude 1, which is analogous to 1 being the basic unit of counting or whole numbers.

In the Cartesian coordinate system (x, y, z in 3D, or just x, y in 2D) the i,j,k or $\hat{x},\hat{y},\hat{z},$ represent mutually orthogonal (perpendicular) orientations or directions. Each is independent of the other.

By linear combinations of the unit vectors, one can define a displacement from some origin.