Match List-I with List -II.

Choose the correct answer from he options given below :

(A)-(III),(B)-(IV),(C)-(II),(D)-(I)

The correct answer is Option (4) → (A)-(III),(B)-(IV),(C)-(II),(D)-(I)

(A) $(\hat{i}×\hat{k}).\hat{j}+(\hat{j}×\hat{k}).\hat{i}$

$=-\hat j.\hat j+\hat i.\hat i=-1+1=0$ (III)

(B) $\hat{i}.(\hat{j}×\hat{k})+\hat{j}.(\hat{i}×\hat{k})+\hat{k}.(\hat{i}×\hat{j})$

$=\hat i.\hat i+\hat j.-\hat j+\hat k.\hat k=1-1+1=1$ (IV)

(C) $(\hat{k}×\hat{j}).\hat{i}+\hat{k}.\hat{j}=-\hat i.\hat i+1=-1$ (II)

(D) $\hat{k}.(\hat{i}×\hat{j})+(\hat{j}×\hat{k}).\hat{i}$

$=\hat k.\hat k+\hat j.\hat j=1+1=2$ (I)