If $\hat i,\hat j$ and $\hat k$, are unit vectors along co-ordinates axes OX, OY and OZ respectively, then which of the following is/are true?

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

Choose the correct answer from the options given below:

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

The correct answer is Option (2) → (A), (C) and (D) only

$\hat i,\hat j,\hat k$ are standard orthonormal unit vectors.

Check each statement:

(A) $\hat i\times \hat i = 0$ because the cross product of any vector with itself is $0$.

(B) $\hat i\times \hat k = -\hat j$, not $\hat j$, so this is false.

(C) $\hat i\cdot \hat i = 1$ because each is a unit vector.

(D) $\hat i\cdot \hat j = 0$ because they are perpendicular.