Home
Class 12
MATHS
Statement 1: The direction cosines of...

Statement 1: The direction cosines of one of the angular bisectors of two intersecting line having direction cosines as `l_1,m_1, n_1a n dl_2, m_2, n_2` are proportional to `l_1+l_2,m_1+m_2, n_1+n_2dot` Statement 2: The angle between the two intersection lines having direction cosines as `l_1,m_1, n_1a n dl_2, m_2, n_2` is given by `costheta=l_1l_2+m_1m_2+n_1n_2dot`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS

    CENGAGE ENGLISH|Exercise Multiple Correct Answers Type|6 Videos
  • VECTORS TRIPLE PRODUCTS, RECIPROCAL SYSTEM OF VECTORS

    CENGAGE ENGLISH|Exercise DPP 2.4|20 Videos

Similar Questions

Explore conceptually related problems

The direction cosines of the lines bisecting the angle between the line whose direction cosines are l_1, m_1, n_1 and l_2, m_2, n_2 and the angle between these lines is theta , are

Find the acute angle between the two straight lines whose direction cosines are given by l+m+n=0 and l^2+m^2-n^2=0

Find the acute angle between the two straight lines whose direction cosines are given by l+m+n=0 and l^2+m^2-n^2=0

The direction cosines of a line equally inclined to three mutually perpendiclar lines having direction cosines as l_(1),m_(1),n_(1),l_(2),m_(2),n_(2) and l_(3), m_(3),n_(3) are

Find the angle between the line whose direction cosines are given by l+m+n=0a n dl^2+m^2-n^2-0.

Find the angle between the line whose direction cosines are given by l+m+n=0a n d2l^2+2m^2-n^2-0.

Find the angle between the line whose direction cosines are given by l+m+n=0a n d2l^2+2m^2-n^2-0.

If 1/2,1/3,n are direction cosines of a line, then the value of n is

Find the angle between the lines whose direction cosines have the relations l+m+n=0 and 2l^(2)+2m^(2)-n^(2)=0 .

Find the angle between the lines whose direction cosines are connected by the relations l+m+n=0a n d2lm+2n l-m n=0.

CENGAGE ENGLISH-VECTOR ALGEBRA-All Questions
  1. If vec a , vec b , vec c , vec d are the position vector of point A ,...

    Text Solution

    |

  2. Show that the points A(6,-7,0),B(16 ,-19 ,-4),C(0,3,-6) and D(2,-5,10)...

    Text Solution

    |

  3. Statement 1: The direction cosines of one of the angular bisectors ...

    Text Solution

    |

  4. Statement 1: In DeltaA B C , vec (A B)+ vec (BC)+ vec (C A)=0 State...

    Text Solution

    |

  5. Statement 1: If vec ua n d vec v are unit vectors inclined at an angl...

    Text Solution

    |

  6. Statement 1: If cosalpha,cosbeta,a n dcosgamma are the direction cosi...

    Text Solution

    |

  7. A vector has components p and 1 with respect to a rectangular Cartesia...

    Text Solution

    |

  8. Statement 1 : If three point P, Q and R have position vectors veca, ve...

    Text Solution

    |

  9. In a four-dimensional space where unit vectors along the axes are h...

    Text Solution

    |

  10. Let A B C be a triangle, the position vectors of whose vertices are -1...

    Text Solution

    |

  11. If non-zero vectors vec a and vec b are equally inclined to coplanar ...

    Text Solution

    |

  12. If A(-4,0,3) and B(14 ,2,-5), then which one of the following points l...

    Text Solution

    |

  13. Prove that the sum of three vectors determined by the medians of a ...

    Text Solution

    |

  14. Prove that the resultant of two forces acting at point O and repres...

    Text Solution

    |

  15. Two forces vec A B and vec A D are acting at vertex A of a quadrilat...

    Text Solution

    |

  16. ABC is a triangle and P any point on BC. If vec(PQ) is the sum of vec(...

    Text Solution

    |

  17. If vector vec a+ vec b bisects the angle between vec a and vec b , ...

    Text Solution

    |

  18. ABCDE is a pentagon. Prove that the resultant of force vec A B , vec...

    Text Solution

    |

  19. if vec (AO) + vec (O B) = vec (B O) + vec (O C) ,than prove that B...

    Text Solution

    |

  20. A unit vector of modulus 2 is equally inclined to x- and y-axes at an ...

    Text Solution

    |