Flashcards in Vectors Deck (54)

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## Vector

### a quantity that has both magnitude and direction

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## Scalar

### only have magnitude

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## Length on a vector

### //u//

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## Displacement

### the distance from start to finish

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## Position Vector

### displacement from point P to origin O

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## 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

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## 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

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## cosine Rule

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

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## Sine Rule

### a/sinA = b/sinB

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## 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

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## When to use cosine rule

### when you have 2 sides and 1 angle

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## When to use sine rule

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

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## Subtraction of Vectors

### u - v = u+(-v)

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## 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

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## 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

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## When to use addition rules

### when you want to know where youll end up

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## When to use subtraction rule

### when you want to know how you got there

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## 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

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## 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

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## dot product

###
is a number denoted by u.v

(length of u)(scalar component of V parallel to u)

/u/ /v2/

/u/ /v/ cos0

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## dot product theta

### angle between the vectors (between 0 and 180)

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