Vectors Flashcards
Vector
a quantity that has both magnitude and direction
Scalar
only have magnitude
Length on a vector
//u//
Displacement
the distance from start to finish
Position Vector
displacement from point P to origin O
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
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
cosine Rule
a^2= b^2 + c^2 - 2bcCosA (capital letters angles)
Sine Rule
a/sinA = b/sinB
Zero Vector
- vector that has no magnitude
denoted by 0
Negative of a vector
in the opposite direction
addition of a negative vector to a positive
a+ - a = 0 vector
When to use cosine rule
when you have 2 sides and 1 angle
When to use sine rule
when you have 2 angles and 1 side or 2 sides and no angle
Subtraction of Vectors
u - v = u+(-v)
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
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
When to use addition rules
when you want to know where youll end up
When to use subtraction rule
when you want to know how you got there
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
Scalar Multiplication - for s less than 0
su has length s times that of u but has opposite direction
