Let `vec(u)=hat(i)-hat(j), vec(v)=2hat(i)+5hat(j), vec(w)= 4 hat(i)+3hat(j) and vec(p) = vec(u) + vec(v)+vec(w)`. Which one of the following is correct ?

If vec(F) = hat(i) + 2hat(j) + hat(k) and vec(V) = 4hat(i) - hat(j) + 7hat(k) find vec(F).vec(V)

If vec(a)=hat(i)-hat(j),vec(b)=hat(j)-hat(k),vec(c)=hat(k)-hat(i)" then find "[vec(a)-vec(b),vec(b)-vec(c),vec(c)-vec(a)]

If vec(F ) = hat(i) +2 hat(j) + hat(k) and vec(V) = 4hat(i) - hat(j) + 7hat(k) what is vec(F) . vec(v) ?

If vec(a)= hat(i) - 2hat(j) + 5hat(k), vec(b)= 2hat(i) +hat(j)- 3hat(k) then what is (vec(a)- vec(b)).(3 vec(a) +vec(b)) equal to ?

If vec(a)= hat(i) - 2hat(j) + 5hat(k) and vec(b) = 2hat(i) + hat(j) -3hat(k) , then (vec(b) - vec(a)).(3 vec(a) +vec(b)) equal to?

If vec(a) . hat(i)= vec(a).(hat(i)+ hat(j)) = vec(a). ( hat(i) + hat(j) + hat(k)) =1 , then vec(a) is equal to

Let vec(u) = hat(i) + hat(j), vec(v) = hat(i) - hat(j) and vec(w) = hat(i) + 2hat(j) + 3hat(k) . If hat(n) is a unit vector such that vec(u).vec(n) = 0 and vec(v).hat(n) = 0 then |vec(w).hat(n)| is equal to.

If vec(a)=hat(i)-2hat(j)+5hat(k) and vec(b)=2hat(i)+hat(j)-3hat(k) then what is (vec(b)-vec(a)). (3vec(a)+vec(b)) equal to ?