# Thread: angle between the vectors ..........

1. ## angle between the vectors ..........

Hello,
plz try to solve that question.Thanks

2. Originally Posted by m777
Hello,
plz try to solve that question.Thanks
a) Ok, so we have two vectors

a = <3, 2, sqrt(3)>
b = <3, 1, sqrt(6)>

We should begin by determining some kind of formula for this:

||a||*||b||cos(x) = a*b

So first we find the magnitude of each of these vectors, which is:

||a|| = (9 + 4 + 3)^.5 = 4

||b|| = (9 + 1 + 6)^.5 = 4

We should also find the dot product of these two vectors:

3*3 + 2*1 + sqrt(9) = 9 + 2 + 3 = 14

So now we plug it all in

4*4 cos(x) = 14

cos(x) = 14/16

cos(x) = .875

arccos(.875) = 28.95 degrees or .505 radians

3. Here's (a)

4. Here's part (b), see Vectors - Cross Product for more info, just do a search for "same plane" by typing Ctrl-F and entering "same plane" in the dialogue box that appears

You may want to check that I found the determinant correctly, I always confuse myself with all the numbers, lol

5. Originally Posted by m777
Hello,
plz try to solve that question.Thanks
Hello,

to b)

3 vectors lie in a plane if you can find values for r and s so that the following equation is true;

r*u + s*v = w

r*<4, -6, 1> + s*<3, 1, -2> = <3, -2, 12>

Transform into a system of linear equations:

4r + 3s = 3
-6r + s = -2
r - 2s = 12

Use the first 2 equations to calculate r and s: r = 9/22 and s = 5/11

Now check if these values satisfy the 3rd equation. Obviously they don't do that. Therefore the 3 vectors are not complanar.

EB

6. Originally Posted by earboth
Hello,

to b)

3 vectors lie in a plane if you can find values for r and s so that the following equation is true;

r*u + s*v = w

r*<4, -6, 1> + s*<3, 1, -2> = <3, -2, 12>

Transform into a system of linear equations:

4r + 3s = 3
-6r + s = -2
r - 2s = 12

Use the first 2 equations to calculate r and s: r = 9/22 and s = 5/11

Now check if these values satisfy the 3rd equation. Obviously they don't do that. Therefore the 3 vectors are not complanar.

EB
I now vaguely remember doing that method when i was in calc 3. Seems easier than my way, in terms of the kind of computation you have to do

the reasoning goes back to linear independence (or something like that) correct?

7. Originally Posted by Jhevon
I now vaguely remember doing that method when i was in calc 3. Seems easier than my way, in terms of the kind of computation you have to do

the reasoning goes back to linear independence (or something like that) correct?
Hello, Jhevon,

you guessed right.

If a poster asks for help here he obviously has some difficulties to understand the math concerning his problem.
So I try to use as much basic math to explain because I believe (and I hope) that at least the basics are understood.
(Somehow I have the impression that this text is far away from being English. Sorry! Do you understand it nevertheless?)

EB

8. Originally Posted by earboth
Hello, Jhevon,

you guessed right.

If a poster asks for help here he obviously has some difficulties to understand the math concerning his problem.
So I try to use as much basic math to explain because I believe (and I hope) that at least the basics are understood.
(Somehow I have the impression that this text is far away from being English. Sorry! Do you understand it nevertheless?)

EB
i understand perfectly earboth.

I always try to do a problem the simplest way as well, unless they ask for a particular method. It's just that i didn't remember you could do it your way. i tend to forget a lot of the math i've gone through, lol. that's one of my reasons for joining this site