explain properties of vector addition
Answers
Step-by-step explanation:
Two vectors are the same if they have the same magnitude and direction. This means that if we take a vector and translate it to a new position (without rotating it), then the vector we obtain at the end of this process is the same vector we had in the beginning.
Two examples of vectors are those that represent force and velocity. Both force and velocity are in a particular direction. The magnitude of the vector would indicate the strength of the force or the speed associated with the velocity.
We denote vectors using boldface as in a or b. Especially when writing by hand where one cannot easily write in boldface, people will sometimes denote vectors using arrows as in a⃗ or b⃗ , or they use other markings. We won't need to use arrows here. We denote the magnitude of the vector a by ∥a∥. When we want to refer to a number and stress that it is not a vector, we can call the number a scalar. We will denote scalars with italics, as in a or b.
You can explore the concept of the magnitude and direction of a vector using the below applet. Note that moving the vector around doesn't change the vector, as the position of the vector doesn't affect the magnitude or the direction. But if you stretch or turn the vector by moving just its head or its tail, the magnitude or direction will change. (
Addition of vectors satisfies two important properties.
The commutative law, which states the order of addition doesn't matter: a+b=b+a. ...
The associative law, which states that the sum of three vectors does not
depend on which pair of vectors is added first: (a+b)+c=a+(b+c)...
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