# Thread: 3D vectors finding perpindicular vector help!!!

1. ## 3D vectors finding perpindicular vector help!!!

hello everybody, first of all i would like to thank you for even trying to help me with my problem, I am doing my 3d vectors homework and I came upon a problem that I am having difficulties with, the problem is as follows:

Determine a vector perpindicular to both the y-axis and the vector AB = [2,-1,2].

any help will be appreciated.

thanks

2. Originally Posted by dmitri
hello everybody, first of all i would like to thank you for even trying to help me with my problem, I am doing my 3d vectors homework and I came upon a problem that I am having difficulties with, the problem is as follows:

Determine a vector perpindicular to both the y-axis and the vector AB = [2,-1,2].

any help will be appreciated.

thanks
The y-axis has a unit vector of <0, 1, 0> and you want a vector mutually perpendicular to this and <2, -1, 2>. Take the cross product of these two vectors.

-Dan

3. Hello, dmitri!

Determine a vector perpendicular to both the y-axis and the vector AB = [2,-1,2].

We have two vectors: . $\begin{array}{ccc}\vec{u} &=&\langle 2,1,2\rangle \\ \vec{v} &=& \langle0,1,0\rangle \end{array}$

A vector perpendicular to both is their cross product.

$\vec{w} \;=\;\vec{u} \times \vec{v} \;=\;\left|\begin{array}{ccc}\bold i&\bold j&\bold k \\ 2&1&2\\0&1&0\end{array}\right| \;=\;\bold i(0-2) -\bold j(0-0) + \bold k(2-0) \;=\;-2\bold i + 2\bold k$

. . Therefore: . $\vec{w} \;=\;\langle -2,0,2\rangle$

4. thanks guys! i appreciate it