What is:
(1, 2, 3)^{T} **×** (0, 0, 0)^{T} ?

### A good answer might be:

Obviously
(1, 2, 3)^{T} **×** **0** = **0**

Or, plug into the formula
**u** **×** **v** =
(
u_{j} v_{k} - u_{k} v_{j} ,
u_{k} v_{i} - u_{i} v_{k} ,
u_{i} v_{j} - u_{j} v_{i}
)^{T}.

(1, 2, 3)^{T} **×** (0, 0, 0)^{T} =
( 2×0 - 3×0, 3×0 - 1×0, 1×0 - 2×0 )^{T} = **0**

# Memory Aid

Here is a way to compute the cross product
by arranging the elements of each vector into a determinant.
The top row contains the symbols that stand for each axes.
This is **not** the definition of cross product.
In fact, it is not even a determinant.
It is merely a memory aid.

This only works for three dimensional vectors
(the cross product is not defined for vectors of any but three dimensions).
Put the **first vector's** components into the second row,
and the **second vector's** components into the third row.

### QUESTION 12:

What is the cross product of (1, 2, 1)^{T} with (0, -1, 2)^{T} ?
Fill in the blanks: