Dig deeper at pwnphysics.blogspot.com

1: The Vector- The arrow in magenta is the vector in question. Everything else in the image serves to describe this vector. It's represented as an arrow and can be slid anywhere in the coordinate system and still retain its properties: the magnitude and direction.

2: Y-Axis- The black vertical arrow represents the y-axis in our coordinate system. This gives a reference point for all of the vectors in our system.

3: Origin- Most physical systems only make sense when there is a point of reference. The intersection of the two axes, is referred to as the origin.

4: Vector Magnitude- In pink arrow is the vector in question. The length of this arrow is referred to as the magnitude.

5: Angle- The angle is a critical part of what makes a vector a vector. Usually denoted by the Greek letter Theta, this provides the direction. Theta is usually given with respect to the positive horizontal axis, but any reference point will provide sufficient direction, making this a vector with both magnitude and direction.

6: Coordinate Representation- Typically, vectors are represented with brackets, e.g. [x,y], so that they are not confused with the same coordinate point represented with parenthesees, (x,y). This point describes the location of the head of the vector, with the tail assumed to be at the origin, (0,0).

7: x-component- The red dashed horizontal arrow is referred to as the x-component of the vector v. This describes 'how much' of the vector is pointed in the x-direction. This makes one leg of a right triangle which describes the vector v, the vector itself being the hypotenuse.

8: X-Axis- The black horizontal arrow represents the x-axis in our coordinate system. This gives a reference point for all of the vectors in our system.

9: y-component- The red dashed vertical arrow is referred to as the y-component of the vector v. This describes 'how much' of the vector is pointed in the y-direction. This makes one leg of a right triangle which describes the vector v, the vector itself being the hypotenuse.

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