Let `vec(alpha)= hat(i) - 2hat(j) + 3 hat(k), vec(b) = hat(i) + hat(j) + hat(k) and vec(c)` be a vector such that `vec(a) + (vec(b) xx vec(c)) = vec(0) and vec(b). vec(c)= 5`. Then the value of `3 (vec(c).vec(a))` is equal to _____

If vec(a) = hat(i) + hat(j) + 2 hat(k) and vec(b) = 3 hat(i) + 2 hat(j) - hat(k) , find the value of (vec(a) + 3 vec(b)) . ( 2 vec(a) - vec(b)) .

If vec(a)=7hat(i)-2hat(j)+3hat(k), vec(b)=hat(i)-hat(j)+2hat(k), vec(c )=2hat(i)+8hat(j) , then find vec(a).(vec(b)xx vec(c )) and (vec(b)xx vec(c )).vec(a) .

If vec(a) = alpha hat(i) + beta hat(j)+ 3 hat(k) , vec(b) = - beta hat(i) - alpha hat(j) - hat(k) and vec( c ) = hat(i) - 2hat(j) - hat(k) such that vec( a) . vec(b) =1 and vec( b ).vec(c ) = - 3 then (1)/(3) ((vec(a) xx vec(b)).vec( c)) is equal to "________" .

If vec(a) = 3 hat(i) + 2 hat(k) , vec(b) = 3hat(j) - hat(k) and vec(c ) = hat(i) + hat(j) + hat(k) . Find ( vec(a) xx vec(b)). vec(c ) .

Let vec(a)= hat(i) +hat(j)+2hat(k) and vec(b)= -hat(i) +2hat(j) +3hat(k) . Then the vector product (vec(a) +vec(b)) xx ((vec(a) xx ((vec(a)-vec(b)) xx vec(b))) xx vec(b)) is equal to

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 ?

Let vec(a) = hat(i) + hat(j) + hat(k),vec(b) = hat(i) - hat(j) + 2hat(k) and vec(c) = xhat(i) + (x-2)hat(j) - hat(k) . If the vector vec(c) lies in the plane of vec(a) and vec(b) then x equals