Space vector

Exercise1.1

1.

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

(1)

$2\boldsymbol{A}$

(2)

$3\boldsymbol{B} - 2\boldsymbol{A}$

(3)

$\vert\boldsymbol{A}\vert$

(4)

$\vert\boldsymbol{A} + \boldsymbol{B}\vert$

2.

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

(1)

$\boldsymbol{A}$ + $\boldsymbol{B}$

(2)

Angle between $\boldsymbol{A}$ and $\boldsymbol{B}$