Match the Column I with Column II and select the option from the given code below
Column I Column II
i. $2 \hat{i} \times (\hat{i} + \hat{j})$ p. $2 \hat{k}$
ii. $4 \hat{i} \times (2 \hat{i} - \hat{j})$ q. 0
iii. $3 \hat{i} \times (3 \hat{i} - 4 \hat{j})$ r. $- 4 \hat{k}$
iv. $2 (\hat{i} + \hat{j}) \times 2 \hat{i}$ s. $- 12 \hat{k}$
Codes

Moderate

Solution

(i) $2 \hat{i} \times (\hat{i} + \hat{j}) = 2 \hat{i} \times \hat{i} + 2 \hat{i} \times \hat{j} = 2 \hat{k}$
(ii) $4 \hat{i} \times (2 \hat{i} - \hat{j}) = 4 \hat{i} \times 2 \hat{i} - 4 \hat{i} \times \hat{j} = 0 - 4 \hat{k} = - 4 \hat{k}$
(iii) $3 \hat{i} \times (3 \hat{i} - 4 \hat{j}) = 3 \hat{i} \times 3 \hat{i} - 12 (\hat{i} \times \hat{j}) = 0 - 12 \hat{k} = - 12 \hat{k}$
(iv) $2 (\hat{i} + \hat{j}) \times 2 \hat{i} = 4 (\hat{i} \times \hat{j}) i + 4 (\hat{j} \times \hat{i}) = 0 + (- 4 \hat{k}) = - 4 \hat{k}$
Hence, (i) $\to (p), (ii) \to (r), (iii) \to (s), (iv) \to (r)$

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