Home
Class 12
MATHS
If vec a , vec b , vec c are non-copla...

If ` vec a , vec b , vec c` are non-coplanar vector and `lambda` is a real number, then the vectors ` vec a+2 vec b+3 vec c ,lambda vec b+mu vec ca n d(2lambda-1) vec c` are coplanar when a. `mu in R` b. `lambda=1/2` c. `lambda=0` d. no value of `lambda`

Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|6 Videos
  • VECTORS TRIPLE PRODUCTS, RECIPROCAL SYSTEM OF VECTORS

    CENGAGE PUBLICATION|Exercise DPP 2.4|20 Videos

Similar Questions

Explore conceptually related problems

If vec a , vec ba n d vec c are non-coplanar vectors, prove that the four points 2 vec a+3 vec b- vec c , vec a-2 vec b+3 vec c ,3 vec a+ 4 vec b-2 vec ca n d vec a-6 vec b+6 vec c are coplanar.

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

If vec a, vec b, vec c are unit vectors satisfying the condition veca+ vec b+ vec c= 0 then show that vec a. vec b+ vec b.vec c+ vec c. vec a= -3//2 .

If vec a , vec ba n d vec c are unit coplanar vectors, then the scalar triple product [2 vec a- vec b2 vec b- vec c2 vec c- vec a] is 0 b. 1 c. -sqrt(3) d. sqrt(3)

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?

If vec(a),vec(b),vec (c ) are non - coplanar vectors vec (r) . vec(a) = vecr . vec(b) = vecr.vec(c ) = 0 , show that vec (r ) is a zero vector .

If vec a , vec b and vec c are three non-coplanar vectors, then ( vec a+ vec b+ vec c).[( vec a+ vec b)xx( vec a+ vec c)] equals a. 0 b. [ vec a vec b vec c] c. 2[ vec a vec b vec c] d. -[ vec a vec b vec c]

If the vectors vec a, vec b, vec c are non-coplanar and l,m,n are distinct real numbers, then [( l vec a + m vec b + n vec c) (l vec b + m vec c + n vec a) (l vec c + m vec a + n vec b )] = 0, implies (A) lm+mn+nl = 0 (B) l+m+n = 0 (C) l^2 + m^2 + n^2 = 0

Let vec a , vec b ,and vec c be any three vectors, then prove that [ vec axx vec b vec bxx vec c vec cxx vec a ]= [vec a vec b vec c]^2

Show that the vectors 2 vec a- vec b+3 vec c , vec a+ vec b-2 vec ca n d vec a+ vec b-3 vec c are non-coplanar vectors (where vec a , vec b , vec c are non-coplanar vectors)

CENGAGE PUBLICATION-VECTOR ALGEBRA-All Questions
  1. A vector oversetrarra has components 2p and 1 with respect to a rectan...

    Text Solution

    |

  2. The sides of a parallelogram are 2 hat i+4 hat j-5 hat k and hat i+2 ...

    Text Solution

    |

  3. If vec a , vec b , vec c are non-coplanar vector and lambda is a re...

    Text Solution

    |

  4. If points hat i+ hat j , hat i- hat j and p hat i+q hat j+r hat k are...

    Text Solution

    |

  5. If the vectors hat i- hat j , hat j+ hat k and vec a form a triangl...

    Text Solution

    |

  6. If the resultant of three forces vec F1=p hat i+3 hat j- hat k , v...

    Text Solution

    |

  7. If vec a, vec b, vec c are unit vectors satisfying the condition veca+...

    Text Solution

    |

  8. The vector hat i+x hat j+3 hat k is rotated through an angle theta an...

    Text Solution

    |

  9. Prove that point hat i +2 hat j - 3 hat k ,2 hat i - hat j + hat k ...

    Text Solution

    |

  10. Show that the point A , B and C with position vectors vec a =3 hat i ...

    Text Solution

    |

  11. If 2vec(AC)=3vec(CB), then prove that 2vec(OA)+3vec(OB)=5vec(OC) where...

    Text Solution

    |

  12. Find the unit vector in the direction of vector vec (PQ), where P and...

    Text Solution

    |

  13. For given vector, vec a = 2 hat i j +2 hat k and vec b = - hat i + ...

    Text Solution

    |

  14. If the projections of vector vec a on x -, y - and z -axes are 2, ...

    Text Solution

    |

  15. Find a vector in the direction of the vector 5 hat i - hat j + 2 h...

    Text Solution

    |

  16. If vec a , vec b , vec c , vec d are the position vector of point A ,...

    Text Solution

    |

  17. Show that the points A(6,-7,0),B(16 ,-19 ,-4),C(0,3,-6) and D(2,-5,10)...

    Text Solution

    |

  18. Statement 1: The direction cosines of one of the angular bisectors ...

    Text Solution

    |

  19. Statement 1: In DeltaA B C , vec (A B)+ vec (BC)+ vec (C A)=0 State...

    Text Solution

    |

  20. If vec aa n d vec b are two vectors of magnitude 1 inclined at 120^0 ...

    Text Solution

    |