Question

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)

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

Determine the vector v, orthogonal to the axis Oy.

Answer 5

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

Answer 6

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

Answer 7

Yes these are dot products

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

And, what´s more?

Answer 12

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

Answer 13

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?

Answer 14

yep

Answer 15

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?

Answer 16

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

Answer 17

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

Answer 18

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

Answer 19

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.

Answer 20

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