Home
Class 12
MATHS
If vec a=5 hat i- hat j-3 hat k ,\ a n ...

If ` vec a=5 hat i- hat j-3 hat k ,\ a n d\ vec b= hat i+3 hat j-5 hat k` then show that the vectors ` vec a+ vec b\ a n d\ vec a- vec b` are perpendicular.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • RELATIONS

    RD SHARMA ENGLISH|Exercise All Questions|197 Videos

  • SCALAR TRIPLE PRODUCT

    RD SHARMA ENGLISH|Exercise All Questions|76 Videos

Similar Questions

Explore conceptually related problems

If vec a=5 hat i- hat j-3 hat k\ a n d\ vec b= hat i+3 hat j-5 hat k , then show that the vectors vec a+ vec b\ a n d\ vec a- vec b are orthogonal.

If vec a= hat i-2 hat j+3 hat k ,\ a n d\ vec b=2 hat i+3 hat j-5 hat k , then find vec axx vec bdot verify that vec a\ a n d\ vec axx vec b are perpendicular to each other.

If vec a= hat i-2 hat j+3 hat k , and vec b=2 hat i+3 hat j-5 hat k , then find vec ax vec b . Verify that vec a and vec ax vec b are perpendicular to each other.

If vec a= hat i-\ hat j+7 hat k and vec b=5 hat i-\ hat j+lambda hat k , then find the value of lambda, so that vec a+ vec b and vec a- vec b are perpendicular vectors.

If vec a=3 hat i- hat j+2 hat k\ a n d\ vec b=2 hat i+ hat j- hat k\ t h e n find ( vec axx vec b) vec adot

If vec p=5 hat i+lambda hat j-3 hat k\ a n d\ vec q= hat i+3 hat j-5 hat k , then find the value of lambda such that vec p+ vec q and vec p- vec q are perpendicular vectors.

If vec a=3 hat i- hat j-2 hat k\ a n d\ vec b=2 hat i+3 hat j+ hat k ,find ( vec a+2 vec b)xx(2 vec a- vec b)dot

Find vec adot vec b when: vec a= hat j- hat k\ a n d\ vec b=2 hat i+3 hat j-2 hat k

If vec a= hat i+3 hat j-2 hat k\ a n d\ vec b=- hat i+3 hat k ,\ find \ | vec axx vec b|dot

If vec a= hat i+ hat j+ hat ka n d vec b= hat i-2 hat j+ hat k , then find vector vec c such that vec adot vec c=2a n d vec axx vec c= vec bdot

RD SHARMA ENGLISH-SCALAR OR DOT PRODUCT-All Questions
  1. Let vec a\ a n d\ vec b be two vectors of the same magnitude such th...

    Text Solution

    |

  2. Find | vec x| if for a unit vector vec a ,\ ( vec x- vec a)dot \ ( ve...

    Text Solution

    |

  3. If vec a=5 hat i- hat j-3 hat k ,\ a n d\ vec b= hat i+3 hat j-5 hat...

    Text Solution

    |

  4. If vec a+ vec b+ vec c= vec0,\ vec|a|=3,\ | vec b|=5\ a n d\ | vec c...

    Text Solution

    |

  5. For any vector vec a\ a n d\ vec b prove that | vec a+ vec b|lt=| ve...

    Text Solution

    |

  6. For any two vectors vec a and vec b prove that ( veca dot vecb)^2le|...

    Text Solution

    |

  7. If vec a ,\ vec b ,\ are two vectors such that | vec a+ vec b|=| ve...

    Text Solution

    |

  8. The scalar product of the vector vec a= hat i+ hat j+ hat k with a un...

    Text Solution

    |

  9. If vec a ,\ vec b ,\ vec c are three vectors such that vec adot ve...

    Text Solution

    |

  10. Show that the vector 2 hat i- hat j+ hat k ,\ hat i-3 hat j-5 hat k ,...

    Text Solution

    |

  11. Show that the points A, B, C with position vectors 2 hat i- hat j+ ...

    Text Solution

    |

  12. If with reference to a right handed system of mutually perpendicula...

    Text Solution

    |

  13. Find the value of x for which the angle between the vectors vec a=2x^...

    Text Solution

    |

  14. If l ,\ m ,\ n are scalars and vec a ,\ vec b ,\ vec c are vectors,...

    Text Solution

    |

  15. If vec a ,\ vec b ,\ vec c are three mutually perpendicular vectors...

    Text Solution

    |

  16. Let vec a ,\ vec b ,\ vec c be three vectors of magnitudes 3, 4 and...

    Text Solution

    |

  17. If vec a ,\ vec b ,\ vec c are unit vectors such that vec a+ vec b...

    Text Solution

    |

  18. Three vectors vec a ,\ vec b ,\ vec c satisfy the condition vec a+...

    Text Solution

    |

  19. Find vec adot vec b when: vec a= hat i-2 hat j+ hat k\ a n d\ vec b...

    Text Solution

    |

  20. Find vec adot vec b when: vec a= hat j+2 hat k\ a n d\ vec b=2 hat ...

    Text Solution

    |