If the equations of two lines L1 and L2 are \vec{r}=\vec{a_1}+λ\vec{b_1} and \vec{r}=\vec{a_2}+μ\vec{b_2}, then which of the following is the correct formula for the angle between the two lines?

(a) cosθ=\left |\frac{\vec{a_1}.\vec{a_2}}{|\vec{b_1}||\vec{a_2}|}\right |

(b) cosθ=\left |\frac{\vec{a_1}.\vec{a_2}}{|\vec{a_1}||\vec{a_2}|}\right |

(c) cosθ=\left |\frac{\vec{b_1}.\vec{b_2}}{|\vec{b_1}||\vec{b_2}|}\right |

(d) cosθ=\left |\frac{\vec{a_1}.\vec{b_2}}{|\vec{a_1}||\vec{b_2}|}\right |

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Query is from Three Dimensional Geometry topic in section Three Dimensional Geometry of Mathematics – Class 12

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The correct option is (c) cosθ=\left |\frac{\vec{b_1}.\vec{b_2}}{|\vec{b_1}||\vec{b_2}|}\right |

The best explanation: Given that the equations of the lines are

\vec{r}=\vec{a_1}+λ\vec{b_1} \,and \,\vec{r}=\vec{a_2}+μ\vec{b_2}

∴ the angle between the two lines is given by

cosθ=\left |\frac{\vec{b_1}.\vec{b_2}}{|\vec{b_1}||\vec{b_2}|}\right |.