MCQ
Let two non-collinear unit vectors $\hat{\mathrm{a}}$ and $\hat{\mathrm{b}}$ form an acute angle. A point $\mathrm{P}$ moves so that at any time $\mathrm{t}$ the position vector $\overline{\mathrm{OP}}$ (where $\mathrm{O}$ is the origin) is given by $\hat{\mathrm{a}} \cos t+\hat{b} \sin t$. When $\mathrm{P}$ is farthest from origin $O$, let $M$ be the length of $\overline{\mathrm{OP}}$ and $\mathrm{u}$ be the unit vector along $\overline{\mathrm{OP}}$. Then,
- ✓$\hat{\mathrm{u}}=\frac{\hat{a}+\hat{b}}{|\hat{a}+\hat{b}|}$ and $M=(1+\hat{a} \cdot \hat{b})^{1 / 2}$
- B$\hat{u}=\frac{\hat{a}-\hat{b}}{|\hat{a}-\hat{b}|}$ and $M=(1+\hat{a} \cdot \hat{b})^{1 / 2}$
- C$\hat{\mathrm{u}}=\frac{\hat{\mathrm{a}}+\hat{\mathrm{b}}}{|\hat{\mathrm{a}}+\hat{\mathrm{b}}|}$ and $\mathrm{M}=(1+2 \hat{\mathrm{a}} \cdot \hat{\mathrm{b}})^{1 / 2}$
- D$\hat{u}=\frac{\hat{a}-\hat{b}}{|\hat{a}-\hat{b}|}$ and $M=(1+2 \hat{a} \cdot \hat{b})^{1 / 2}$