Question $1(20$ Marks$)$

$($a$)$ Find the unit vector along the line joining point $(2,4,4)$ to $(4$ marks$)$

point $(-3,2,2).$

$($b$)$ Let $A=2a_x+5a_y-3a_z,B=3a_x-4a_y,$ and $C=a_x+a_y+a_z.$

i$.$ Determine $A+2B.$

$(2$ marks$)$

ii$.$ Calculate $|A-5C|.$

$(3$ marks$)$

iii. Find $\frac{AB}{A-B}.$

$(6$ marks$)$

$($c$)$ If $A=2a_x+a_y-3a_z,B=a_y-a_z,$ and $C=3a_x+5a_y+7a_z.$

i$.A-2B+C.$

$(2$ marks$)$

ii$.C-4(A+B).$

$(3$ marks$)$