Solve this following
Question:

Let $\overrightarrow{\mathrm{a}}=\hat{\mathrm{j}}-\hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{c}}=\hat{\mathrm{i}}-\hat{\mathrm{j}}-\hat{\mathrm{k}}$. Then the vector $\overrightarrow{\mathrm{b}}$ satisfying $\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{c}}=\overrightarrow{0}$ and $\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{b}}=3$ is :

1. $-\hat{\mathrm{i}}+\hat{\mathrm{j}}-2 \hat{\mathrm{k}}$

2. $2 \hat{\mathrm{i}}-\hat{\mathrm{j}}+2 \hat{\mathrm{k}}$

3. $\hat{\mathrm{i}}-\hat{\mathrm{j}}-2 \hat{\mathrm{k}}$

4. $\hat{i}+\hat{j}-2 \hat{k}$

Correct Option: 1

Solution: