Question $4$

$($a$)$ Let $a=-3i+j+k$ and $b=2i-2j+k$ be two vectors of $R^3.$ Use vector method$($s$)$ to find

$($i$)$ the projection of a onto $b.$

$(4$ marks$)$

$($ii$)$ the smaller angle between a and $b.$ Correct the answer to $NE$ decimal place. $(4$ marks$){?}_{(})$

$($iii$)$ the area of the triangle determined by a and $b.$

$(4$ marks$)$

$($b$)$ Find the maximum and minimum values of the function $3x+4y$ on the circle $x^2+y^2=1.$

$(13$ marks$)$