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:
Answer & explanation
Correct answer: option 2
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.
final answer: the correct options are (A), (C), and (D)