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## Ignore words

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vector
the direction or course followed by an airplane, missile, or the like
column vector/ vector
a matrix with only one column
Vectors in R ^2
the set of all vectors with two entries; ordered pairs of real numbers
Equal vectors
Two vectors w/ the same length and direction
parallelogram rule for addition: u + v
If u and v are represented as points in a plane, u + v corresponds to the 4th vertex of the parallelogram whose other vertices are u, 0, and v
Vectors in R ^3
3 x 1 column matrices with three entries; represented as points in a 3D coordinate space
Vectors in R^n
collection of all lists of n real numbers written as n x 1 column matrices
linear combination
Vector y defined as y = c1v1 + ... + cpvp where c's are weights, v's are vectors
span {v1, ..., vp}
the set of all scalar multiples of v, ... vp; if the vector equation/ augmented matrix has a solution, then v is in the span
i
Represents the horizontal value of a vector in an equation.
j
Represents the vertical value of a vector in an equation.
(q₁-p₁, q₂-p₂)
Component Form of a Vector with initial Point P = (p₁, p₂) and terminal point Q = (q₁,q₂)
√(q₁-p₁)²+(q₂-p₂)²
Magnitude of a Vector with initial Point P = (p₁, p₂) and terminal point Q = (q₁,q₂)
(1/(||v||))v
How to find a Unit Vector
Unit Vector
a vector with a magnitude of 1. the positive X-axis is vector i, pos. <1,0> y xis is vector j <0,1>
Component Form, add i for horizontal and j for vertical
First to find the "i + j" for a vector, you find this of the 2 points and then...
tan⁻¹(j/i)
How to find direction angle of vectors given the j+i form
tan⁻¹(y/x)
How to find direction angle of vectors given the x and y form
(magnitude)(cos(angle))i+(magnitude)(sin(angle))j
Given Angle + Magnitude, formula for Component Form
(q₁-p₁)i + (q₂-p₂)j
Unit Form of a Vector with initial Point P = (p₁, p₂) and terminal point Q = (q₁,q₂)
Distance
Given magnitude and direction and trying to find a vector, first use this equation.
divide it by the magnitude
Given magnitude and direction and trying to find a vector, after using the distance equation, you do this to the number.
(Given Magnitude/Found Magnitude)(Points)
Given magnitude and direction and trying to find a vector, this is the last thing you do [equation].
√((F₁+F₂cos(Ө))² + (F₂sin(Ө)²) = Resultant Force
Given 2 forces and a resultant force, and trying to find the angle, use this formula.
(u₁v₁) + (u₂v₂)
The dot product of u = (u₁,u₂) and v = (v₁,v₂) is given by u · v =
cos(Ө) = (u · v)/(magnitude of u * magnitude of v)
If Ө is the angle between two nonzero vectors u and v, then this is the formula to find the angle between TWO vectors.
orthogonal
If the dot product is 0, the two vectors are...
the magnitude of vector V squared
Taking the dot product of vector V by itself will yield...
Component Form, Dot Product
When given 2 vectors and a force (trying to find work), first find this of the 2 vectors and take that point and find this with the force.
Distance Formula
Formula for Magnitude of : v=-4i-7j
Tan Formula
Formula for Direction of : v=-4i-7j