Geometric vectors and vector space

Exercise1-2

1. For vectors A = $(2,-1,3)$ and B = $(-1,1,4)$, find the followings:

(a) ${\bf A} + {\bf B}$ (b) $3{\bf B}$ (c) $\Vert{\bf A}\Vert$ (d) $3{\bf B} - 2{\bf A}$

2. For vectors A = $(-2,-1,3)$ and B = $(3,0,1)$, express the following vectors using ${\bf i},{\bf j},{\bf k}$ ．

(a) ${\bf B} - {\bf A}$ (b) $3{\bf A} + {\bf B}$ (c) $3{\bf B} - 2{\bf A}$ (d) $${\frac{{\bf A} + {\bf B}}{2}}$$

3. Show that geometric vectors defined in 1.1 satifies the properties 1 thru 5．

4. Show that geometric vectors defined in 1.1 satifies the properties 6 thru 9．

5. Show that geometric vectors defined in 1.1 satifies the properties 1 thru 9. ． 6. Two vectors ${\bf A}$ and ${\bf B}$ have the same initial point. Find the vector ${\bf C}$ which disect the angle between ${\bf A}$ and ${\bf B}$. 7. Solve the equation $x(1,1,1) + y(1,1,0) + z(1,0,0) = (2,-3,4)$. Find $x, y, z$.