Home
Class 12
MATHS
Prove that the measure of the angle betw...

Prove that the measure of the angle between two main diagonals of a cube is `cos^(-1)frac[1][3]`.

Text Solution

Verified by Experts

The correct Answer is:
`cos^(-1)((1)/(3))`
Promotional Banner

Topper's Solved these Questions

  • QUESTION PAPER 2018

    ARIHANT PUBLICATION|Exercise SHORT ANSWER TYPE QUESTIONS (ANSWER ANY THREE QUESTIONS)|38 Videos

  • PROBABILITY

    ARIHANT PUBLICATION|Exercise CHAPTER PRACTICE(LONG ANSWER TYPE QUESTIONS)|17 Videos

  • QUESTION PAPER 2019

    ARIHANT PUBLICATION|Exercise Group C (30 Marks) |13 Videos

Similar Questions

Explore conceptually related problems

Prove the following by vector method. Measure of the angle between two diagonals of a cube is cos^-1 (1/3)

Prove the angle between the diagonal of one of the faces of the cube and the diagonal of the cube intersecting the diagonal of the face of the cube is cos^(-1)"sqrt(2/3)

If veca makes equal angles with hati, hatj and hatk and has magnitude 3, prove that the angle between veca and each of hati, hatj and hatk is cos^(-)(1/sqrt3) .

ARIHANT PUBLICATION-QUESTION PAPER 2018-SHORT ANSWER TYPE QUESTIONS (ANSWER ANY THREE QUESTIONS)
  1. int(0)^(1/2)(1)/(sqrt(1-x^(2)))dx.

    Text Solution

    |

  2. Find the area enclosed bt the two paraboles y^2=4 ax and x^2=4ay.

    Text Solution

    |

  3. Prove that the measure of the angle between two main diagonals of a cu...

    Text Solution

    |

  4. The position vectors of two points A and B are 3hati+hatj+2hatk and ha...

    Text Solution

    |

  5. Find the area of the triangle ABC with vertices A(1,2,4), B(3,1,-2) an...

    Text Solution

    |

  6. Prove that [(veca+vecb,vecb+vecc,vecc+veca)]=2[(veca,vecb,vecc)].

    Text Solution

    |

  7. If the sum of two unit vectors is a unit vector, show that the magnitu...

    Text Solution

    |

  8. If a=2hati+hatk,b=hati+hatj+hatkandc=4hati-3hatj+7hatk, then find the ...

    Text Solution

    |

  9. Find the shortest distance between the lines (x-3)/3=(y-8)/(-1)=(z-3)/...

    Text Solution

    |

  10. int(0)^(1)(1)/(1-x^(2))dx.

    Text Solution

    |

  11. Let f:XrightarrowY and g:YrightarrowZ. Prove that gof is bijective if ...

    Text Solution

    |

  12. In a DeltaABC, if mangleA=90^(@), prove that "tan"^(-1)b/(a+c)+"tan"^(...

    Text Solution

    |

  13. By elementary operations, find A^(-1) for the following: A=[[1,1,0],[1...

    Text Solution

    |

  14. Solve the following system of equations by the matrix inversion method...

    Text Solution

    |

  15. Two cards are drawn successively with replacement from a well-shuffled...

    Text Solution

    |

  16. Find the coordinates of the point on the curve x^2y - x + y = 0 wher...

    Text Solution

    |

  17. If x = (1-cos^2 theta)/(cos theta), y = (1-cos^(2n)theta)/(cos^n theta...

    Text Solution

    |

  18. Find the solution of the following differential equations: (4x+6y+5)dx...

    Text Solution

    |

  19. Evaluate intfrac[2cosx+7][4-sinx]dx

    Text Solution

    |

  20. Find the area enclosed by y=4x-1 and y^(2)=2x.

    Text Solution

    |