- #1
LCSphysicist
- 646
- 161
- Homework Statement
- All below, well
- Relevant Equations
- All below
That is, the triad forms a basis.
What does this notation mean, particularly '^'?LCSphysicist said:[a,b,c] = a ^ b . c
Infrared said:It means the scalar triple product, ##[a,b,c]=(a\times b)\cdot c.##
A vector is a mathematical object that has both magnitude (size) and direction. It is typically represented by an arrow pointing in the direction of its magnitude.
The components of a vector are the individual parts that make up its magnitude and direction. These are typically represented as the x and y coordinates of the vector's tip, with the origin (0,0) being the vector's tail.
Writing the components of a vector in a specific way allows for easier manipulation and calculation of the vector's properties. It also allows for the vector to be easily graphed and visualized.
The components of a vector are written as (x,y) because this notation corresponds to the position of the vector's tip in the x-y plane. The x component represents the horizontal distance from the origin, while the y component represents the vertical distance.
Yes, the components of a vector can also be written in terms of other coordinate systems, such as polar coordinates. In this case, the components would be written as (r, θ), where r is the vector's magnitude and θ is the angle it makes with the positive x-axis.