Question

Find two vectors parallel A and perpendicular A that add up to A such that one is parallel and one is perpendicular to B.

Let A= i-3j+2k and B=2i-4k.

So since A= parallel A + perpendicular A, I worked out parallel A to be { -1, 0, 2} and perpendicular A to be {0, -3, 0}. But I don't understand how to relate that back to B.

The answers are (-3/5)i + (6/5)k and (8/5)i + (-3)j +(4/5)k

Answer 1

i cant make out the instructions that well

Answer 2

if parallel A is over A and thru A under over with a dash of per A on the sid eof A then we want to A the addition of A and blah blah blah .... who came up with this mess?

Answer 3

http://math.scu.edu/~gmohler/practicemidterm2_math13.pdf

it's problem #3 to this worksheet

Answer 4

burn your worksheet lol

Answer 5

does parallel and perp have to be parallel and perp to A? or is that just what they wanted to go as a naming convention?

Answer 6

I'm assuming it's just a naming convention

Answer 7

its a terrible convention then; but otherwise how would you get 2 vectors that add up to A otherwise right

Answer 8

I found parallel A by using projB A = (AB/ BB) B

Answer 9

perp would be B.A

Answer 10

or at least a vector named perpA i think

Answer 11

ah, I'll try that and see

Answer 12

perpA.B = 0 if that makes sense

Answer 13

subtract your //A from A and see if it pers with B by chance

Answer 14

that would give me perpendicular A

Answer 15

it might

Answer 16

if i see it right, and thats a big if, i get something akin to

\[n<2,0,-4>\ + <2,0,-4>*<a,b,c>=<1,-3,2>\]

Answer 17

to me this means that:
\[n<2,0,-4>\ + 0\ =<1,-3,2>\]
\[2n=1;\ 0=-3;\ -4n=2\] that doesnt seem right does it

Answer 18

i see what i did, i dotted in the wrong spot lol

Answer 19

<a,b,c> is spose to add to n<2,0,-4> and get <1,-3,2>

<a,b,c> is spose to dot to <2,0,-4> and equal 0

Answer 20

I found in my notes that perpendicular A + //A = A; and perpendicular A x B = 0. But how would the latter help me?

Answer 21

prove to me you found //A, show me your steps so i can chk it

Answer 22

LA and //A are good for symbols

Answer 23

//A = ProjB A = (2+0-8)/(4+8) x {2, 0, -4} = -1/2 x {2, 0, -4} = {-1, 0, 2}

Answer 24

and then I did LA = A - //A

so LA = {1, -3, 2} - {-1, 0, 2} = {0, -3, 0}

Answer 25

i did this:
\[nB = //A =<2n,0,-4n>\]
\[//A+<a,b,c>=A<1,-3,2>\]
\[\begin{array}l
2n+a=1\ a=1-2n\\
0n+b=-3;\ b=-3\\
-4n+c=2;\ c=2+4n
\end{array}\]

<1-2n , -3, 2+4n>
< 2 , 0 , -4 >
-------------------
2-4n +0 -8-16n = 0

-6 -20n = 0

-20n=6

n= -6/20 = -3/10

Answer 26

oh wait, I made a mistake

Answer 27

(-3/10) <2,0,-4> = <-3/5 , 0 , 6/5>

which is what your answer shows

Answer 28

thats //A

Answer 29

A - //A = LA, it has to

Answer 30

8/5i -3j+4/5k

Answer 31

thank you so much! :D

Answer 32

your welcome, i hope it made sense :)