Level 436
Level 438

#### 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.

**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