Home
Class 12
MATHS
If vec a and vec b are non-collinear ve...

If ` vec a` and `vec b` are non-collinear vectors and vectors ` vecalpha=(x+4y) vec a+(2x+y+1) vec b` and `vecbeta=(-2x+y+2) vec a+(2x-3y-1) vec b` are connected by the relation `3 vecalpha=2 vecbeta`,find the value of x and y?

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • ALGEBRA OF MATRICES

    RD SHARMA ENGLISH|Exercise All Questions|410 Videos
  • APPLICATION OF INTEGRALS

    RD SHARMA ENGLISH|Exercise All Questions|163 Videos

Similar Questions

Explore conceptually related problems

If vec aa n d vec b are non-collinear vectors, find the value of x for which the vectors vecalpha=(2x+1) vec a- vec b""a n d"" vecbeta=(x-2)"" vec a+ vec b are collinear.

Vectors vec aa n d vec b are non-collinear. Find for what value of x vectors vec c=(x-2) vec a+ vec b and vec d=(2x+1) vec a- vec b are collinear?

Vectors vec a and vec b are non-collinear. Find for what value of n vectors vec c=(n-2) vec a+ vec b and vec d=(2n+1) vec a- vec b are collinear?

veca , vec b , vec c are non-coplanar vectors and x vec a + y vec b + z vec c = vec 0 then

If vec a and vec b are two non-collinear unit vectors such that | vec a+ vec b|=sqrt(3), find (2 vec a-5 vec b). (3 vec a+ vec b) .

If vec a and vec b are two non-collinear vectors having the same initial point. What are the vectors represented by vec a+ vec b and vec a- vec b .

If vec a and vec b are two non-collinear vectors having the same initial point. What are the vectors represented by vec a+ vec b and vec a- vec b .

If vec a\ a n d\ vec b are two non collinear unit vectors such that | vec a+ vec b|=sqrt(3),\ find \ (2 vec a-5 vec b). (3 vec a+ vec b)

If vec a and vec b be two non-collinear unit vector such that vec axx( vec axx vec b)=1/2 vec b , then find the angle between vec a and vec b .

If vec a , vec b are two non-collinear vectors, prove that the points with position vectors vec a+ vec b , vec a- vec b and vec a+lambda vec b are collinear for all real values of lambdadot

RD SHARMA ENGLISH-ALGEBRA OF VECTORS-All Questions
  1. A vector vec r is inclined at equal to O X ,O Ya n dO Zdot If the mag...

    Text Solution

    |

  2. A vector vec r has length 21 and its direction ratios are proport...

    Text Solution

    |

  3. If vec a and vec b are non-collinear vectors and vectors vecalpha=(x...

    Text Solution

    |

  4. A B C D is a parallelogram. E ,F are mid-points of B C ,C D respective...

    Text Solution

    |

  5. If a\ a n d\ b ar non collinear vector such that x1 vec a+y1 vec b=x2 ...

    Text Solution

    |

  6. Show that the vectors a, b, c given by vec a= hat i+2 hat j+3 hat k ,...

    Text Solution

    |

  7. A vector vec O P is inclined to O X at 50^0 and O Y at 60^0 . Find th...

    Text Solution

    |

  8. If a vector makes angles alpha,beta,gamma. with . OX ,O Ya n dO Z ...

    Text Solution

    |

  9. A B C D is a parallelogram. If L and M are the mid-points of B C and D...

    Text Solution

    |

  10. Find a unit vector in the direction of the resultant of the vectors...

    Text Solution

    |

  11. Find the position vector of the mid-point of the vector joining the...

    Text Solution

    |

  12. Show that the line joining one vertex of a parallelogram to the mid...

    Text Solution

    |

  13. Let vec a , vec b, vec c be three non-zero vectors such that any two ...

    Text Solution

    |

  14. If vec a , vec b are the position vectors of the points (1,-1),(-2,m...

    Text Solution

    |

  15. Find the position vector of a point A in space such that vec O A is i...

    Text Solution

    |

  16. Show that the points A(6,-7,0),B(16 ,-19 ,-4),C(0,3,-6)a n d D(2,-5,1...

    Text Solution

    |

  17. Prove that the lines joining the vertices of a tetrahedron to the ce...

    Text Solution

    |

  18. Find a vector vec r of magnitude 3sqrt(2)u n i t s which makes an an...

    Text Solution

    |

  19. Let vec a= hat i+2 hat ja n d vec b=2 hat i+ hat jdoti s |vec a|=| ve...

    Text Solution

    |

  20. Three vectors of magnitude a ,2a ,3a meet in a point and their directi...

    Text Solution

    |