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:
Answer & explanation
Correct answer: option 4
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)