Prove that
(i) `[hat(i)hat(j)hat(k)]=[hat(j)hat(k)hat(i)]=[hat(k)hat(j)hat(i)]=1`
(ii)`[hat(i)hat(k)hat(j)]=[hat(k)hat(j)hat(i)]=[hat(j)hat(i)hat(k)]=1`

Prove that [hat(i)hat(j)hat(k)]=1, and [hat(i)hat(k)hat(j)]=-1 .

[[hat(i), hat(j), hat(k)]]+[[hat(k), hat(j), hat(i)]]+[[hat(j), hatk, hat(i)]]=

(hat(k)xx hat(j)).hat(i)+hat(j).hat(k)= ………….

hat(i)*(hat(j)timeshat(k))+hat(j)*(hat(k)timeshat(i))+hat(k)*(hat(i)timeshat(j))=

Find the value of : (i) (hat(i) xxhat(j))*hat (k) + hat(i)* hat(j) (ii) (hat(k) xx hat(j))* hat(i) +hat(j)* hat(k) hat(i) xx (hat(j) + hat(k) )+hat(j) xx(hat(k) +hat(i))+ hat(k) xx (hat(i)+hat(j))

Write the value of hat(i).(hat(j)xxhat(k))+hat(j).(hat(i)xxhat(k))+hat(k).(hat(i)xxhat(j)) .

If a=hat(i)+hat(j)+hat(k) and b=hat(i)-hat(j) , then the vectors (a*hat(i))hat(i)+(a*hat(j))hat(j)+(a*hat(k))hat(k), (b*hat(i))hat(i)+(b*hat(j))hat(j)+(b*hat(k))hat(k) and hat(i)+hat(j)-2hat(k)

(hat i xxhat j)*hat k+(hat j+hat k)*hat j