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

Prove that hat(i).(hat(j)xx hat(k))=1 .

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

Evaluate [hat(i) hat(k) hat(j)] + [hat(i) hat(j)hat(k)] .

Find the angle between hat(i)+hat(j)+hat(k) and hat(i)+hat(j)-hat(k) .

Let a=hat(i)+hat(j)+hat(k), b=-hat(i)+hat(j)+hat(k), c=hat(i)-hat(j)+hat(k) and d=hat(i)+hat(j)-hat(k) . Then, the line of intersection of planes one determined by a, b and other determined by c, d is perpendicular to

A vector perpendicular to (hat(i)+hat(j)+hat(k)) and (hat(i)-hat(j)-hat(k)) is :-

If the vectors a hat(i) + hat(j) + hat(k), hat(i) + b hat(j) + hat(k) and hat(i) + hat(j) + c hat(k) (a,b ne 1) are coplanar then the value of (1)/(1-a) + (1)/(1-b) + (1)/(1-c) is equal to

What is the value of lambda for which the vectors hat(i)-hat(j)+hat(k), 2 hat(i)+hat(j)-hat(k) and lambda hat(i)-hat(j)+lambda hat(k) are co-planar?