## viniterranova 3 years ago Find a vector perpendicular to Oy axis. Knowing that v*v1=8 and v*v2=-3. v1=(3,1,-2) and v2=(-1,1,1)

1. Spacelimbus

A bit confused by this question, is this what you have written above the dot product? the x-axis is perpendicular to the y-axis, also the z-axis

2. TuringTest

...or any other vector in the without a y component

3. TuringTest

oh wait, it's supposed to be perpendicular to which axis? @viniterranova please explain so we can help you

4. viniterranova

Determine the vector v, orthogonal to the axis Oy.

5. viniterranova

where v*v1=8 and v*v2=-3

6. TuringTest

you did not really clarify you just repeated yourself are these dot products?

7. viniterranova

Yes these are dot products

8. viniterranova

9. Spacelimbus

then the y component can be left away, will result in a system of equations.

10. viniterranova

Here it´s a shot from the book where i taken the question.

11. TuringTest

so we have$\vec v\cdot\vec v_1=8$$\vec v\cdot\vec v_2=-3$where$\vec v_1=\langle3,1,-2\rangle$$\vec v_2=\langle-1,1,1\rangle$and if it is perpendicular to the y axis we have that$\vec v\cdot\langle0,1,0\rangle=0$let$\vec v=\langle x,y,z\rangle$ and we get the system of equations spacelimbus was referring to

12. viniterranova

And, what´s more?

13. TuringTest

$\vec v\cdot\vec v_1=3x+y-2z=8$$\vec v\cdot\vec v_2=-x+y+z=-3$$\vec v\cdot\langle0,1,0\rangle=y=0$

14. viniterranova

So, in this case y = zero? That ´s right? So, i just plug 0 in the equation in order to slove the system? Am i right?

15. TuringTest

yep

16. viniterranova

In this i got a following system 3x-2z=8 and -x+z= -3 and solving in function of z i got z=x-3 and so, i have reached x=2. Am i right?

17. Spacelimbus

x=2, z=-1, is what I got if you want to compare.

18. viniterranova

Yes, that´s for sure. x=2 and z=-1. Thanks guys.

19. viniterranova

So the answer to the question is w=(2,0,-1)

20. Spacelimbus

well in the exercise they called the vector v, so you maybe want to name him like that too, but that's not a convention, the coordinates are what's important, and you maybe want to write it in brackets, see how @TuringTest wrote the vectors.

21. viniterranova

Thanks for the help. But, i don´t know how to use the Latex yet. Thanks a lot for the help.