Home
Class 12
MATHS
Find the all the values of lamda such th...

Find the all the values of lamda such that (x,y,z)!=(0,0,0)`and `x(hati+hatj+3hatk)+y(3hati-3hatj+hatk)+z(-4hati+5hatj)=lamda(xhati+yhatj+zhatk)`

Text Solution

Verified by Experts

The correct Answer is:
`lambda=0,lambda=-2+-sqrt(29)`
Promotional Banner

Topper's Solved these Questions

  • VECTOR

    MOTION|Exercise EXERCISE - 4 ( LEVEL -I)|36 Videos

  • TRIGONOMETRIC EQUATION

    MOTION|Exercise EXERCISE 4|10 Videos

Similar Questions

Explore conceptually related problems

The value of lambda in R such that (x, y, z) ne (0, 0, ) and (2hati+3hatj-4hatk)x+(3hati-hatj+2hatk)y+(i-2hatj)z=lambda(xhati+yhatj+zhatk) lies in

If (x,y,z) ne (0,0,0) and (hati + hatj +3hatk )x + (3 hati - 3 hatj + hatk )y +(-4 hati + 5 hatj ) z = a (x hati + y hatj + z hatk ), then the values of a are

Find the value of lamda so that the two vectors 2hati+3hatj-hatk and -4hati-6hatj+lamda hatk are parallel

Find the values of x,y and z so that vectors veca=xhati+4hatj+zhatk and vecb=3hati+yhatj+hatk are equal.

Find the value of lamda so that the two vectors 2hati+3hatj-hatk and -4hati-6hatj+lamda hatk are Perpendicular to each other

The lines vecr=(hati+hatj)+lamda(hati+hatk)andvecr=(hati+hatj)+mu(-hati+hatj-hatk) are

Find the angle between the line: vecr=4hati-hatj+lamda(hati+2hatj-2hatk) and vevr=hati-hatj+2hatk-mu(2hati+4hatj-4hatk)

The equation of plane containing the lines barr=(2hatj-3hatk)+lamda(hati+2hatj+3hatk) barr=(2hati+6hatj+3hatk)+lamda(2hati+3hatj+4hatk)

The value of lambda, for which the four points 2hati+3hatj-hatk, hati-2hatj+3hatk, 3hati+4hatj-2hatk, hati-6hatj+lambda hatk are coplanar, is

MOTION-VECTOR -EXERCISE - 4 ( LEVEL-II)
  1. If veca, vecb and vecc are three unit vectors such that veca xx (vecb ...

    Text Solution

    |

  2. The diagonals of a parallelogram are given by vectors 2hati+3hatj-6hat...

    Text Solution

    |

  3. Find the all the values of lamda such that (x,y,z)!=(0,0,0)and x(hati+...

    Text Solution

    |

  4. Two vertices of a triangle are at -hati+3hatj and 2hati+5hatj and its ...

    Text Solution

    |

  5. If veca, vecb, vecc are unit vectors, then |veca-vecb|^2+|vecb-vec|^2+...

    Text Solution

    |

  6. Let veca=hati-hatk, vecb=xhati+hatj+(1-x)hatk and vecc=yhati+xhatj+(1+...

    Text Solution

    |

  7. Let vec A(t) = f1(t) hat i + f2(t) hat j and vec B(t) = g(t)hat i+g2(...

    Text Solution

    |

  8. If veca and vecb are two unit vectors such that veca+2vecb and 5veca-4...

    Text Solution

    |

  9. Let vecV=2hati+hatj-hatk and vecW=hati+3hatk. It vecU is a unit vector...

    Text Solution

    |

  10. The value of a so that the volume of the paralelopiped formed by hati+...

    Text Solution

    |

  11. A unit vector int eh plane of the vectors 2hati+hatj+hatk, hati-hatj+h...

    Text Solution

    |

  12. If veca=veci+vecj+veck, veca.vecb=1 and vecaxxvecb=vecj-veck, then vec...

    Text Solution

    |

  13. If veca,vecb,vecc,vecd are four distinct vectors satisfying the condit...

    Text Solution

    |

  14. Let veca=hati + 2hatj +hatk, vecb=hati - hatj +hatk andvecc= hathatj-h...

    Text Solution

    |

  15. Let vecA be a vector parallel to the of intersection of planes P1 and ...

    Text Solution

    |

  16. The number of distinct values of lamda, for which the vectors -lamda^(...

    Text Solution

    |

  17. Let veca, vecb ,vecc be unit vetors such that veca + vecb + vecc = ve...

    Text Solution

    |

  18. Assertion: vec(PQ)xx(vec(RS)+vec(ST))!=0, Reason : vec(PQ)xxvec(RS)=ve...

    Text Solution

    |

  19. The edges of a parallelopiped are of unit length and are parallel to n...

    Text Solution

    |

  20. Lelt two non collinear unit vectors hata and hatb form and acute angle...

    Text Solution

    |