Home
Class 12
MATHS
Prove that 1,1,1 cannot be direction cos...

Prove that 1,1,1 cannot be direction cosines of a straight line.

Text Solution

AI Generated Solution

To prove that \(1, 1, 1\) cannot be direction cosines of a straight line, we will follow these steps: ### Step 1: Understanding Direction Cosines Direction cosines of a straight line are defined as the cosines of the angles that the line makes with the coordinate axes. If a line has direction cosines \(L\), \(M\), and \(N\), then they must satisfy the equation: \[ L^2 + M^2 + N^2 = 1 \] ...
Promotional Banner

Topper's Solved these Questions

  • ALGEBRA OF MATRICES

    RD SHARMA|Exercise Solved Examples And Exercises|410 Videos
  • APPLICATION OF INTEGRALS

    RD SHARMA|Exercise Solved Examples And Exercises|118 Videos

Similar Questions

Explore conceptually related problems

Direction cosine and ratio of line

If the directions cosines of a straight line are ltk,k,kgt then

A line passes through the point (3, 1,2) and (5,-1,1) , find the direction cosines of the line.

If P-=(1,2,3) then direction cosines of OP are

If the direction ratio of a line is 1,-2,2 Then what are the direction cosines of the line

If the direction cosines of a straight line are l,m and n, then prove that l^(2)+m^(2)+n^(2)=1

l = m = n = 1 are the direction Cosines of

For what value 'a' will the number sqrt(1/2),a,sqrt(1/3) be the direction cosines of a line?

Lines OA,OB are drown from O with direction cosines proportinal to 1,-2,-1;3-2,3. Find the direction cosines of the normal to the plane AOB .

RD SHARMA-ALGEBRA OF VECTORS-Solved Examples And Exercises
  1. Prove that the following vectors are non-coplanar: 3 hat i+ hat j- ...

    Text Solution

    |

  2. Using vectors show that the points A(-2,3,5),B(7,0,-1)C(-3,-2,-5) and ...

    Text Solution

    |

  3. Prove that 1,1,1 cannot be direction cosines of a straight line.

    Text Solution

    |

  4. A vector vec r is inclined at equal acute angles of x-a xi s , y-a...

    Text Solution

    |

  5. Find the angles at which the following vectors are inclined to each...

    Text Solution

    |

  6. Find the direction cosines of the following vectors: 2 hat i+2 hat...

    Text Solution

    |

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

    Text Solution

    |

  8. If P is a point and A B C D is a quadrilateral and vec A P+ vec...

    Text Solution

    |

  9. If vec a is a vector and m is a scalar such that m vec a= vec0 ...

    Text Solution

    |

  10. If vec a , vec b are two vectors, then write the truth value of th...

    Text Solution

    |

  11. A B C D is a quadrilateral. Find the sum the vectors vec B A , ve...

    Text Solution

    |

  12. A B C D E is pentagon, prove that vec A B + vec B C + vec C D ...

    Text Solution

    |

  13. If P ,Q and R are three collinear points such that vec P Q= vec a ...

    Text Solution

    |

  14. Give a condition that three vectors vec a , vec b and vec c from ...

    Text Solution

    |

  15. If vec a and vec b are two non-collinear vectors having the same ...

    Text Solution

    |

  16. Find the magnitude of the vector vec a=2 hat i+3 hat j-6 hat kdot

    Text Solution

    |

  17. Find the unit vector in the direction of 3 hat i+4 hat j-12 hat kdo...

    Text Solution

    |

  18. The vertices A , B , C of triangle A B C have respectively position ...

    Text Solution

    |

  19. Find a unit vector parallel to the vector hat i+sqrt(3) hat j

    Text Solution

    |

  20. Show that the found points A ,B ,C ,D with position vectors vec a , v...

    Text Solution

    |