Originally Posted by

**Paymemoney** Hi

Can someone tell me where i have gone wrong in the following question?

Given that **v**=2**i** + 2**j** + **k**, **w** = 3**i** - **j** + **k** find a unit vector perpendicular to both **v** and **w**.

unit vector = {**a** x **b**}/{|**a** x **b**|}

| **a x b **|=$\displaystyle \sqrt{3^2+1^2+8^2}$

$\displaystyle =\sqrt{74}$

**a x b** = **i**(2 x 1 - 1 x -1)-**j**(2 x 1 - 1 x 3)+**k**(2 x -1 - 2 x 3)

=**i**(2+1)-**j**(2-3)+**k**(-2-6)

=3**i**+**j**-8**k**

therefore unit vector = $\displaystyle \frac{1}{\sqrt{74}}$(3**i**+**j**-8**k**)

answer says its$\displaystyle \frac{1}{\sqrt{74}}$(-3**i**-**j**+8**k**)

P.S