i searched google and everything and nothing really explains this at all..

the topic is ~vectors~

component form of a vector-

how do you write the component form?

in my notes it says "the component form of a vector with initial point P(x1,y1) and terminal point Q(x2,y2) is ->PQ=

<x2-x1, y2-y1>"

what the hell does that mean...

and then what is

the magnitude of a vector?

again.. my notes say "the magnitude (length) is given by |->PQ|=

~(x2-x1)*squared*+(y2-y1)*squared* ~

***and all of the stuff between the two"~" is under a radical

does this make anysence at all?

if so..

heres the first example... it says..

"find the component form and magnitude of the vector "v" that has the initial point (4,-7) and terminal point (-1,5)"

can anyone explain how to go about solving that?

thanks to anyone who has any idea about vectors..

i searched everywhere and found nothing and i know some of you UG'ers are fairly smart. Any help would be great

thx.
v CLICK v

Quote by musicjunkie207
The time I fell on my face on a trampoline and cracked my neck, then proceded to run around the yard in a blind panic screaming "I hope I'm not paralyzed! OH GOD I THINK I'M PARALYZED!"
i-component: Distance in the x-direction from the first to second point
= X2 - X1
j-component: Distance in the y-direction from the first to second point
= Y2 - Y1

I'm guessing the form your teacher wants it in is < i , j >

so the answer would be (-1-4)i + (5-(-7))j

or -5i+13j

or <5,13>

As for magnitude:

It's sqrt[( i^2 )+( j^2 )]

Or in this example, sqrt[5^2+13^2]

or sqrt[194]

or 13.93
Last edited by RockThe40oz at Mar 20, 2007,
it's straight plugging in numbers. ~(-1-5)squared+(-7-5)squared~
~(-6)squared+(-12)squared~
~36+144~
~180~
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Quote by RockThe40oz

As for magnitude:

It's sqrt[(i^2)+(j^2)]

Or in this example, sqrt[5^2+13^2]

or sqrt[194]

or 13.93

ok i get the component form now... but idk where the hell any of that came from ^

EDIT: ahhh got it now.. thx mate.. ill see how things turn out
v CLICK v

Quote by musicjunkie207
The time I fell on my face on a trampoline and cracked my neck, then proceded to run around the yard in a blind panic screaming "I hope I'm not paralyzed! OH GOD I THINK I'M PARALYZED!"
Last edited by GibsonRocker14 at Mar 20, 2007,
Quote by GibsonRocker14
ok i get the component form now... but idk where the hell any of that came from ^

It's just something you have to memorize.

Or you could think of it as a triangle.

The x ( i - component) would be one leg (a)

The y ( j - component) would be another leg (b)

The magnitude would be the hypotenus. (c)

So c^2 = a^2 + b^2 (Pythagorean Theroum)

or (take square root of both sides)

c = sqrt[( a ^ 2 ) + ( b ^ 2 )]

Now replace it with M (magnitude), i and j:

M = sqrt[( i ^ 2 ) + ( j ^ 2 )]
awww shoot. i just found one last thing.

though it doesnt look soo hard.. i dont know where to start.

it says

"let v=<-2,5> and w= <3,4>, find the following:"

A. w+v

B. v-w

C. 2v

how would i solve those?
v CLICK v

Quote by musicjunkie207
The time I fell on my face on a trampoline and cracked my neck, then proceded to run around the yard in a blind panic screaming "I hope I'm not paralyzed! OH GOD I THINK I'M PARALYZED!"
anybody?? ^
v CLICK v

Quote by musicjunkie207
The time I fell on my face on a trampoline and cracked my neck, then proceded to run around the yard in a blind panic screaming "I hope I'm not paralyzed! OH GOD I THINK I'M PARALYZED!"
B. do the components of V minus the components of W (ie V add negative W)
C. Multiply the components of V by two.

In the end its just like simple algebra, but each letter (v and w) correspond to two values which define a vector. Vectors have magnitude and direction. In this case they are defined with their components. Imagine that the start of the vector is at the origin of a graph, and the two numbers (components) are an ordered pair that plots the end of the vector. To add the vectors just place them head to tail, so if they are in component form you can just add the corresponding component values together.

Its kinda hard to explain just here :S
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