## Class/Course - Class XII

### Subject - Math

#### Chapter - Vector Algebra

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Q.1 Let two non-collinear unit vectors $\hat{a}$ and $\hat{b}$ form an acute angle. A point P moves so that at any time t the position vector $\overrightarrow{OP}$ (where O is the origin) is given by $\hat{a}cost + \hat{b}sint$. When P is farthest from origin O, let M be the length of $\overrightarrow{OP}$ and $\hat{u}$ be the unit vector along $\overrightarrow{OP}$. Then, | |

$\hat{u}$ = $\frac{\hat{a} + \hat{b}}{\left | \hat{a} + \hat{b} \right |}$ $and M = \left (1 + \hat{a}.\hat{b} \right )^{1/2}$ | |

$\hat{u}$ = $\frac{\hat{a} - \hat{b}}{\left | \hat{a} - \hat{b} \right |}$ $and M = \left (1 + \hat{a}.\hat{b} \right )^{1/2}$ | |

$\hat{u}$ = $\frac{\hat{a} + \hat{b}}{\left | \hat{a} + \hat{b} \right |}$ $and M = \left (1 + 2\hat{a}.\hat{b} \right )^{1/2}$ | |

$\hat{u}$ = $\frac{\hat{a} - \hat{b}}{\left | \hat{a} - \hat{b} \right |}$ $and M = \left (1 + 2\hat{a}.\hat{b} \right )^{1/2}$ | |