Inner product

Exercise1.2

1.

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

(1)

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

(2)

A unit vector with the direction of $\boldsymbol{A}$

2.

For ${\bf A}= 2{\bf i} + 2{\bf j} - {\bf k}$ and ${\bf B} = -{\bf i} -4{\bf j} - {\bf k}$, find the followings.

(1)

Inner product of ${\bf A}$ and ${\bf B}$

(2)

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