vectors Flashcards
what do vectors have
direction and magnitude (length)
what is magnitude
the length of displacement
what is a scaler
it is a normal number which can be used to scale a vector eg a can double to become 2a and the scalar would be 2
how to prove a vector is parallel
prove one is a multiple of the other. find a scalar multiplier to get from one to the other
how to write a vector in terms of I and J
i is the top number and J is the bottom number
i is the x direction and J is the Y direction
eg
2 =2i +j
1
4 = 4i-9j
-9
what does |AB| or |a| or |b| mean you need to work out
the magnitude (length) of the vector
(using Pythagoras)
what is a unit vector and how do we get it
a unit vector is vector with a magnitude of 1
we get it by using Pythagoras to work out the magnitude of the vector. whatever the magnitude is of the vector you divide it by or jst multiply by 1/itself to the original vector to get the unit vector of that vector.
eg magnitude of vector 3
4 is 5 so just divide that vector by 5 so the vector has a magnitude of 1 or jst times vector by 1/5
what angle do we measure for the direction of a vector
the angle created from the x axis to the vector anticlockwise
go from the x axis anticlockwise until you hit the vector dotted line.
how to draw a dotted vector line from a vector
join up the two lines from your vector using dotted line to form the triangle.
start from where you started (x) to the end of the y line pointing towards the y line
basically join from where you started to where you ended
What angles to measure when asked for the angle the vector makes with the direction of i and the direction of j
From the start of the vector line you should draw the i direction and the j direction
I goes straight up and j goes straight to the side
What does on a bearing of 027 mean (example)
Draw a straight north arrow up
Then do the degrees clockwise from the north arrow
what does write in component form mean
in terms of i and j
how to show that points lie on a straight line
show they are parallel (one is a multiple of the other)
when using position vectors how do we find the vector between two points
where we are - where we started
eg BC= position vector c - position vector b
BC = OC - OB
O= origin
what does displacement vector AB mean
from A to B
not the same as the position vector of AB
