Home
Class 12
MATHS
Find the range of f(x)=sin^(-1)x+tan^(-1...

Find the range of `f(x)=sin^(-1)x+tan^(-1)x+cos^(-1)xdot`

Text Solution

Verified by Experts

Three vectors are coplanar when their scalar triple product is `0.`
`=> [veca vecb vecc] = 0`
`=>|[1,-1,1],[2,1,-1],[lambda,-1,lambda]| = 0`
`=>[1(lambda-1)+1(3lambda)+1(-2lambda -1)] = 0`
`=>lambda-1+3lambda-2lambda-1 = 0`
`=> 2lambda = 2`
`=>lambda = 1`, for which these three vectors will be coplanar.
Promotional Banner

Topper's Solved these Questions

  • SCALAR OR DOT PRODUCT

    RD SHARMA ENGLISH|Exercise All Questions|233 Videos
  • SOLUTION OF SIMULTANEOUS LINEAR EQUATIONS

    RD SHARMA ENGLISH|Exercise All Questions|114 Videos

Similar Questions

Explore conceptually related problems

Range of f(x)=sin^(-1)x+tan^(-1)x+sec^(-1)x is

Find the range of f(x)=|x-1|-1

Find the range of f(x) = cos^(-1) x + cot^(-1) x

Range of f(x)=sin^(- 1)x+sec^(- 1)x is

Find the domain and range of f(x)=sin^(-1)x+tan^(-1)x+sec^(-1)x.

Find the range of f(x)=sin^2x-sinx+1.

Find the range of f(x)=sin^2x-sinx+1.

Find the range of f(x) = (sin^(-1) x)^(2) + 2pi cos^(-1) x + pi^(2)

Find the range of f(x)=|3tan^(-1)x-cos^(-1)(0)|-cos^(-1)(-1)dot

Find the range of f(x)=|3tan^(-1)x-cos^(-1)(0)|-cos^(-1)(-1)dot

RD SHARMA ENGLISH-SCALAR TRIPLE PRODUCT -All Questions
  1. If the vectors vecalpha=a hat i+a hat j+c hat k , vecbeta= hat i+ hat...

    Text Solution

    |

  2. Determine alpha such that a vector vec r is at right angles to each o...

    Text Solution

    |

  3. Find the range of f(x)=sin^(-1)x+tan^(-1)x+cos^(-1)xdot

    Text Solution

    |

  4. If vec a , vec b , vec c are three non-coplanar vectors, prove that [...

    Text Solution

    |

  5. For any three vectors a b,c, show that vec a xx (vec b +vec c)+vec b x...

    Text Solution

    |

  6. Let vec a , vec b , vec c be three non-zero vectors such that vec c ...

    Text Solution

    |

  7. Let vec a , vec ba n d vec c , be non-zero non-coplanar vectors. Prov...

    Text Solution

    |

  8. Find the altitude of a parallelepiped determined by the vectors ve...

    Text Solution

    |

  9. Let vec a , vec b , vec c , be three non-zero vectors. If vec a .(ve...

    Text Solution

    |

  10. If the vectors vecalpha=a hat i+ hat j+ hat k , vecbeta= hat i+b hat ...

    Text Solution

    |

  11. If a is a non-zero real number, then prove that the vectors vecalph...

    Text Solution

    |

  12. If vec a+vec b+vec c=0, prove that (vec a xx vec b)=(vec b xx vec c)=(...

    Text Solution

    |

  13. Show that the vectors vec a=-2 hat i-2 hat j+4 hat k ,\ vec b=-2 ...

    Text Solution

    |

  14. Find lambda so that the vectors vec a=2 hat i- hat j+ hat k ,\ vec b...

    Text Solution

    |

  15. The four points whose position vector are 6 hat i - 7 hat j,16 hat i -...

    Text Solution

    |

  16. For any three vectors a ,\ b ,\ c prove that [ vec a+ vec b\ vec b...

    Text Solution

    |

  17. Show that vectors vec a ,\ vec b ,\ vec c are coplanar if vec a+ v...

    Text Solution

    |

  18. Show that the vectors vec a - vec b, vec b - vec c , vec c - vec a are...

    Text Solution

    |

  19. What can you conclude about four non zero vectors vec a ,\ vec b ...

    Text Solution

    |

  20. Evaluate the following: [ hat i\ hat j\ hat k]+[ hat j\ hat k\ ...

    Text Solution

    |