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IB DP Maths: AA HL復(fù)習(xí)筆記3.9.2 Position & Displacement Vectors

Category: IB課程, 教材筆記, 福利干貨 Date: 2022年7月12日下午4:36

To?add?or?subtract?vectors numerically simply add or subtract each of the corresponding components
In?column vector?notation just add the top, middle and bottom parts together
In?base vector?notation add each of the?i,?j, and?k?components together separately
- For example: (2i?+?j?– 5k)?– (i?+ 4j?+ 3k) = (i?– 3j?– 8k)

11.1.3-Vector-Addition-Diagram-1b

Vectors can be?added?geometrically by joining the end of one vector to the start of the next one
The?resultant?vector will be the shortest route from the start of the first vector to the end of the second
- A?resultant?vector is a vector that results from?adding?or?subtracting?two or more vectors
If the two vectors have the same?starting position, the second vector can be?translated?to the end of the first vector to find the resultant vector
- This results in a?parallelogram?with the resultant vector as the diagonal
?To?subtract?vectors, consider this as?adding on the negative vector
- For example:?a?–?b?=?a?+ (-b)
- The end of the?resultant vector a – b?will not be anywhere near the end of the vector?b
  - Instead, it will be at the point where the end of the vector?-b?would be

Working in column vectors tends to be easiest when adding and subtracting
- in your exam, it can help to convert any vectors into column vectors before carrying out calculations with them
If there is no diagram, drawing one can be helpful to help you visualise the problem

3-9-2-ib-aa-hl-add--sub-vectors-we-solution-a-

A position vector describes the?position?of a point in relation to the?origin
- The origin is always denoted O
The individual components of a position vector are the coordinates of its end point
- For example the point with coordinates (3, -2, -1) has position vector 3i?– 2j?–?k

Determine the position vector of the point with coordinates (4, -1, 8).

3-9-2-ib-aa-hl-position-vector-we-solution

A?displacement vector?describes the shortest route between any two points
- It describes the?direction?and the?distance?between any two points