A vector $\overrightarrow{a}$ of length $2$ units is making an angle $60°$ with each of the $X$-axis and $Y$-axis. If another vector $\overrightarrow{b}$ of length $\sqrt{2}$ units is making an angle $45°$ with each of the $Y$-axis and $Z$-axis, then $\overrightarrow{a}\times \overrightarrow{b}=$

• Correct answer
  A

  $(1-\sqrt{2})\hat{i}-\hat{j}+\hat{k}$
• B

  $\hat{i}-\sqrt{2}\hat{j}+\hat{k}$
• C

  $\sqrt{2}\hat{i}-\hat{j}+2\hat{k}$
• D

  $\hat{i}-2\hat{j}+(1-\sqrt{2})\hat{k}$

Hence, the correct answer is option: 'A'.