$($a$)[2$ marks$]$ Given the vectors a $=$ i $+$ j $+$ k$,$ b $=2$i $+3$j $+4$k find whether they are perpendicular or not by computing their scalar product. $($b$)[3$ marks$]$ Given the vectors a $=5$i $+2$j $+$ k$,$ b $=10$i $4$j $2$k find whether they parallel or not by computing their vector product. $($c$)[2$ marks$]$ Find a vector parallel to a $=5$i $+3$j$,$ with magnitude $10$