If $\hat i,\hat j$ and $\hat k$ are unit vectors along the co-ordinate axes OX, OY and OZ respectively, then

(A) $\hat i×\hat j = \hat k$
(B) $\hat k×\hat i = -\hat j$
(C) $\hat j.\hat j=1$
(D) $\hat j.\hat k = 0$

Choose the correct answer from the options given below:

(A), (C) and (D) only

The correct answer is Option (4) → (A), (C) and (D) only

(A) $\hat i×\hat j = \hat k$
(C) $\hat j.\hat j=1$
(D) $\hat j.\hat k = 0$

Given unit vectors î, ĵ, and k̂ along OX, OY, and OZ:

(A) î × ĵ = k̂ → True  (using right-hand rule)

(B) k̂ × î = −ĵ → False, since k̂ × î = ĵ

(C) ĵ · ĵ = 1 → True  (dot product of unit vector with itself is 1)

(D) ĵ · k̂ = 0 → True  (dot product of perpendicular vectors is 0)