Answer
a x b = 0i-18j-18k
a and b are orthogonal to a x b
Work Step by Step
a=<3,3,-3>, b=<3,-3,3>
a x b is equal to the determinant of the matrix:
| i j k |
| 3 3 -3 |
| 3 -3 3 |
This can be found using the formula
When plugging values into this formula, you get
<0i,-18j,-18k>
The cross product of two vectors will result in a vector orthogonal to both, which we can use to check
a*(a x b)=<3,3,-3>*<0,-18,-18>=0-54+54=0
b*(a x b)=<3,-3,3>*<0,-18,-18>=0+54-54=0
Because both of these equations equal zero, it confirms that a x b is orthogonal to both a and b
