Vectors Flashcards
What are vectors?
Vectors are quantities that have both magnitude (size) and direction.
Give examples of vector quantities
-Velocity
-Displacement
-Acceleration
Column vectors
Represented as vertical columns, such as (⁵₃) indicating movement of 5 units right and 3 units up.
Bold notation
Used in textbooks and exams, represented by bold characters like a.
Arrow notation
Represented as → with AB underneath showing a vector going from point A to point B.
Underlined (a type of vector notation)
Represented as a letter underlined, such as a.
What happens when vectors are multiplied by scalars (numbers) ?
The size of the vector changes, but its direction remains the same.
What do positive scalars do?
Scale up the vector while keeping the direction the same.
What do negative scalars do?
Reverse the direction of the scalar.
Be careful of…
…NEGATIVES
What is a resultant vector?
A new vector made when two vectors are combined through addition or subtraction.
What letter denotes a resulting vector?
R or this underlined if the a and b are
How do we add vectors?
Align them tip to tail and the resulting vector runs from the tail of the first vector to the tip of the second.
How do we subtract vectors?
Subtracting a vector is like adding its negative; it involves reversing the direction of the second vector before adding.
b = a - c in a triangle
What does the magnitude of a vector tell us?
The size (length) of the vector.
How do we find the length (magnitude/modulus) of a vector?
Use Pythagoras’ theorem
How do we represent the length/magnitude/modulus of a vector?
I_I with an a in the middle
How do we calculate the magnitude of the vector (⁵₃)
a = √1² + 5² = 5.10
What is it worth doing when calculating the magnitude of a vector?
Drawing out the known sides as lengths in a triangle before trying to use Pythagoras’ theorem.
How do we use vectors to find an unknown length?
Identify the route for the vector you want to find.
Substitute the known vectors.
If an arrow goes from C to D but on your route you go from D to C, what does this mean?
you need a - CD
What does the top number in a column vector mean?
How many squares to the right or left (if negative)?
What does the bottom number in a column vector mean?
How many squares up or down (if negative)?
What must we always do when writing a vector as a letter e.g. a in an exam?
UNDERLINE THE LETTER (because you can’t make it bold)
Vectors that are scalar multiples of each other (e.g. 2a and -1.5a) are…
parallel
what does a+b mean?
go along a and then b
what does a-b mean?
go along a and then backwards along b
