Cross product

Exercise1.3

1.

For $\boldsymbol{A} = {}^t[1\ 2\ 1], \boldsymbol{B} = {}^t[2\ -1\ -2]$，find $\boldsymbol{A} \times \boldsymbol{B}$．

2.

For $\boldsymbol{A} = 2\:\boldsymbol{i} - 3\:\boldsymbol{j} - \:\boldsymbol{k},\ \boldsymbol{B} = \:\boldsymbol{i} + 4\:\boldsymbol{j} - 2\:\boldsymbol{k}$，find the following vectors:．

(1)

$\boldsymbol{A} \times \boldsymbol{B}$

(2)

$(2\boldsymbol{A} - 3\boldsymbol{B}) \times (\boldsymbol{A} + 2\boldsymbol{B})$

3.

Let $\boldsymbol{A} = \:\boldsymbol{i} + 2\:\boldsymbol{j} + \:\boldsymbol{k}, \boldsymbol{B} = 2\:\boldsymbol{i} - \:\boldsymbol{j} - 2\:\boldsymbol{k}$．Find the followings.

(1)

The area of the parallelogram when ${\bf A}$ and ${\bf B}$ are regarded as two adjacent sides．

(2)

vector other than the zero vector that is orthogonal to ${\bf A}$ and ${\bf B}$.