# Thread: two unit vectors orthogonal

1. ## two unit vectors orthogonal

find two unit vectors orthogonal to both

<1, -1, 1> and <0, 4, 4>

can ya run down through this problem please.

there were square roots in the answer, i thought this was just dot product?

thanks.

2. Originally Posted by rcmango
find two unit vectors orthogonal to both

<1, -1, 1> and <0, 4, 4>

can ya run down through this problem please.

there were square roots in the answer, i thought this was just dot product?

thanks.
o_O showed you how to do the cross product.

$\displaystyle (1,-1,1) \times (0,4,4) = (-8,-4,4)$

Now calculate the absolute value of the resulting vector:

$\displaystyle |(-8,-4,4)| = \sqrt{96}=4\sqrt{6}$

Divide the result by the absolute value to reduce the vector to the length 1:

$\displaystyle \overrightarrow{u_1} = \dfrac{(-8,-4,4)}{4\sqrt{6}} = (-2\sqrt{6}, -\sqrt{6}, \sqrt{6})$

$\displaystyle \overrightarrow{u_2} = \dfrac{(-8,-4,4)}{-4\sqrt{6}} = (2\sqrt{6}, \sqrt{6}, -\sqrt{6})$

3. thanks, ya was cross product not dot product.

used (-4 -4) - (4-0) + (4-0)

for -8, -4. 4

thankyou, especially for the breakdown on the rest of the problem.