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Flashcards in Vectors Deck (54)
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1

Vector

a quantity that has both magnitude and direction

2

Scalar

only have magnitude

3

Length on a vector

//u//

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Displacement

the distance from start to finish

5

Position Vector

displacement from point P to origin O

6

Vector Addition - Head to tail

Step 1: move the second vector until its tail touches the head of the first vector
Step 2: form the vector joining the tail of the first to the head of the second, this is now a+b

7

Vector Addition - Parallelogram Rule

Step 1: move the vectors a and b until their tails collide at a common origin
Step 2: complete a parallelogram based on a and b as 2 adjacent sides
Step 3: the vector from opposite corner of the parallelogram to origin is the sum of a and b

8

cosine Rule

a^2= b^2 + c^2 - 2bcCosA (capital letters angles)

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Sine Rule

a/sinA = b/sinB

10

Zero Vector

- vector that has no magnitude
denoted by 0

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Negative of a vector

in the opposite direction

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addition of a negative vector to a positive

a+ - a = 0 vector

13

When to use cosine rule

when you have 2 sides and 1 angle

14

When to use sine rule

when you have 2 angles and 1 side or 2 sides and no angle

15

Subtraction of Vectors

u - v = u+(-v)

16

Vector subtraction Rule: Head to Tail

Step 1: Reverse the sense of v to create
Step 2: move (-V) so that its tail lies at the head of u
Step 3: join the tail of u to the head of (-v) to form u+(-v) = u - v

17

Vector subtraction Rule: Tail to Tail

Step 1: move v parallel to itself so that its tail touches the tail of u
Step 2: draw the vector from the head of v to the tail of u, this is u-v

18

When to use addition rules

when you want to know where youll end up

19

When to use subtraction rule

when you want to know how you got there

20

Scalar Multiplication -for s greater or equal to 0

the product SU is defined to be a vector in the same direction as u but with the length s times as long

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Scalar Multiplication - for s less than 0

su has length s times that of u but has opposite direction

22

Unit Vectors

has the same direction of u but has the length of one unit ((1/IuI) x u)

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Angle Between Vectors

the lesser of the 2 possible angles between u and v

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u + v

v+u

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(u+V) + w

u + (v + w)

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u + 0

0 + u = u

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u + (-u)

0

28

dot product

is a number denoted by u.v
(length of u)(scalar component of V parallel to u)
/u/ /v2/
/u/ /v/ cos0

29

dot product theta

angle between the vectors (between 0 and 180)

30

Scalar Components - V2

/v/ cos0 (parallel)