Question

vectors again and again

Answer 1

use vector to find the point that lies two thirds of the way from point P(4,3,0) to Q(1,-3,3)

Answer 2

Use points P and Q to make a component vector. Find the magnitude of this vector. Then multply the magnitude of the vector by the appropriate amount so that the magnitude is 2/3 of the original.

Answer 3

ok so it will be
<-3,-6,3> then magnitude would be 3sqrt(2)

Answer 4

now i am confused

Answer 5

3 sqrt(6) ****

Answer 6

\[\sqrt{9+36+9}= \sqrt{54}=3\sqrt{6} \]Lol, you corrected it.

Answer 7

haha i noticed that error after

Answer 8

So now all we need to do is multiply this magnitude by 2/3.

Answer 9

2 sqrt(6)

Answer 10

I guess I was looking at the question. That is the distance from the point P to the point 2/3 of the way there. I guess I thought the question was different at first.

Answer 11

oh so you know how to solve it?

Answer 12

Guess not x_x I didnt read the question well enough. I could probably figure it out, but the others out there would knwo what to do immediately where I have to think, haha.

Answer 13

haha ok

Answer 14

Yeah, I have an answer, but who knows, lol.

Answer 15

i know the answer but not the way

Answer 16

If you got the answer, then id like to see. I wanna see how miserably far off I am xDD

Answer 17

(2,-1,2) is the answer but i don't know how to get there

Answer 18

Yeah, thats what I got x_x My way worked but I doubt its the proper method xD

Answer 19

not to worry, help me how you got there

Answer 20

Yeah, sure. Well, I did what we did at first, found the component vector of <-3.-6,3> I realized thattheres no reason to find the magnitude, all we need to do is multiply these 3 points by 2/3. So this gives us <-2, -4, 2>. Now this helps us get 2/3 of the distance, but we're still not at the spot of our original vector. In order to get back, I added back onto to our vector what I took away in order to get the component vector. We did
<1-4, -3-3, 3-0> So instead I added back 4, added back 3, added back 0. That way Im now lined up with where I was lined up originally. So added those figures to the 2/3 vector I have, I do <-2 + 4, -4 + 3, 2 + 0>, which gets us <2, -1, 2>
Not the best method, but it worked x_x

Answer 21

drawing wud help visualize