## viniterranova Group Title 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) 2 years ago 2 years ago

1. Spacelimbus Group Title

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 Group Title

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

3. TuringTest Group Title

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

4. viniterranova Group Title

Determine the vector v, orthogonal to the axis Oy.

5. viniterranova Group Title

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

6. TuringTest Group Title

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

7. viniterranova Group Title

Yes these are dot products

8. viniterranova Group Title

9. Spacelimbus Group Title

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

10. viniterranova Group Title

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

11. TuringTest Group Title

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 Group Title

And, what´s more?

13. TuringTest Group Title

$\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 Group Title

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 Group Title

yep

16. viniterranova Group Title

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 Group Title

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

18. viniterranova Group Title

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

19. viniterranova Group Title

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

20. Spacelimbus Group Title

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 Group Title

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