Let A be a point in space such that $\left|\overline{\mathrm{OA}}\right| = 12$ where O is the origin. If $\overline{\mathrm{OA}}$ is inclined at angles 45^o and 60⁰ with x-axis and y-axis respectively, then what is $\overline{\mathrm{OA}}$ equal to ?

• $6\hat{\mathrm{j}} +\hspace{0.17em}6\hat{\mathrm{i}} + 2\hat{\mathrm{k}}$

• $6\sqrt{2}\hat{\mathrm{i}} +\hspace{0.17em}6\hat{\mathrm{j}} \pm 6\hat{\mathrm{k}}$

• $6\sqrt{2}\hat{\mathrm{j}} +\hspace{0.17em}6\hat{\mathrm{i}} \pm 6\hat{\mathrm{k}}$

• $3\sqrt{2}\hat{\mathrm{j}} +\hspace{0.17em}3\hat{\mathrm{i}} \pm 6\hat{\mathrm{k}}$

If $\hat{\mathrm{a}}$ is a unit vector in the xy-plane making an angle 30^o with the positive x-axis, then what $\hat{\mathrm{a}}$ is equal to

• $\frac{\sqrt{3}\hat{\mathrm{i}} + \hat{\mathrm{j}}}{2}$

• $\frac{\sqrt{3}\hat{\mathrm{i}} - \hat{\mathrm{j}}}{2}$

• $\frac{\hat{\mathrm{i}} + \sqrt{3}\hat{\mathrm{j}}}{2}$

• $\frac{\hat{\mathrm{i}} - \sqrt{3} \hat{\mathrm{j}}}{2}$