Which of the following is the correct formula for the angle between two planes?

(a) cosθ=\left |\frac{\vec{n_1}.\vec{n_2}}{|\vec{n_1}||\vec{n_2}|}\right |

(b) sinθ=\left |\frac{\vec{n_1}.\vec{n_2}}{|\vec{n_1}||\vec{n_2}|}\right |

(c) cosθ=\left |\frac{\vec{n_1}+\vec{n_2}}{|\vec{n_1}||\vec{n_2}|}\right |

(d) sinθ=\left |\frac{\vec{n_1}+\vec{n_2}}{(|\vec{n_1}|+|\vec{n_2}|}\right |

I have been asked this question during a job interview.

This key question is from Three Dimensional Geometry topic in section Three Dimensional Geometry of Mathematics – Class 12

NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options

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The correct option is (a) cosθ=\left |\frac{\vec{n_1}.\vec{n_2}}{|\vec{n_1}||\vec{n_2}|}\right |

For explanation I would say: If two planes of the form \vec{r}.\vec{n_1}=d_1 and \vec{r}.\vec{n_2}=d_2 where \vec{n_1} \,and \,\vec{n_2} are the normals to the plane, then the angle between them is given by

cosθ=\left |\frac{\vec{n_1}.\vec{n_2}}{|\vec{n_1}||\vec{n_2}|}\right |