(Solved): Question \( 1.2 \) Two sets of basis vectors are given: 1. \( e_{\mathrm{x}}=(1,0,0), \boldsymbol{ ...

Question \( 1.2 \) Two sets of basis vectors are given: 1. \( e_{\mathrm{x}}=(1,0,0), \boldsymbol{e}_{\mathrm{Y}}=(0,1,0), \boldsymbol{e}_{\mathrm{2}}=(0,0,1) \) 2. \( \boldsymbol{g}_{\mathrm{x}}=\left(\frac{1}{2} \sqrt{2}, 0, \frac{1}{2} \sqrt{2}\right), \boldsymbol{g}_{\mathrm{y}}=(0,1,0), \boldsymbol{g}_{\mathrm{z}}=\left(-\frac{1}{2} \sqrt{2}, 0, \frac{1}{2} \sqrt{2}\right) \) A point \( Q \) is given by \( \boldsymbol{q}=2 \boldsymbol{g}_{\mathrm{x}}+\boldsymbol{g}_{\mathrm{y}}+2 \boldsymbol{g}_{\mathrm{z}} \). Express the vector \( \boldsymbol{q} \) as a linear combination of the basis vectors \( \boldsymbol{e}_{\mathrm{x}}, \boldsymbol{e}_{\mathrm{y}}, \boldsymbol{e}_{\mathrm{z}} \).