11. Vectors Flashcards
How to write vector AB
—>
AB
Magnitude of vector a
a |
If two vectors have the same magnitude and direction
They are the same vector and are parallel
Adding vectors
–> —> —>
AB + BC = AC but |AB| + |BC| ≠ |AC|
0 vector
No displacement
How to write a vector parallel to vector a
λa where λ is a scalar
Unit vector
A vector whose magnitude is 1
a^2 + b^2 = 1
Basis unit vector
A unit vector that is parallel with either the x or y axis
i vector
( 1 )
0
j vector
( 0 )
1
Vector ci + dj
( c )
d
Magnitude-direction form
Defining a vector by giving it’s magnitude and its angle from one of the coordinate axes (usually anti-clockwise from i)
How to write θ if 180 < θ < 360
-180 < θ < 0
a when a = (r, θ) and θ is measured anti-clockwise from positive i
( r cosθ)
r sinθ
a
Unit vector parallel to a
a
—-
|a|
Notation of position vector A
—>
OA
How to find the position vector of A
Put the x and y coordinates into a vector
—–>
How to find vector AB from position vectors
—-> —->
OB - OA
Unit vector in the direction of u formula
u
û = ———
|u|
Bisect
Cross in the middle to cut in half
How to show the ratio a line is divided into
Write the same vector in different ways using scalars λ and μ for the vector it is part of the way along
Set the coefficients of a and b equal and solve
Finding the angle between vectors
Form a triangle and use cosine rule with the magnitude of each
Velocity
a
—– x speed
|a|
Angle between 3d vector a = xi + yj + zk and the x, y or z axis
axis value/|a|
Area of a 3d triangle
Find the magnitude of each vector, use cosine rule to find an angle and use 1/2 ab sinC
