Level 436 Level 438
Level 437

Vector Equations


31 words 0 ignored

Ready to learn       Ready to review

Ignore words

Check the boxes below to ignore/unignore words, then click save at the bottom. Ignored words will never appear in any learning session.

All None

Ignore?
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